--------------------------------------------------------
      name:  PSRM
       log:  D:\Replication.log
  log type:  text
 opened on:   2 Oct 2021, 18:04:55

. use ExperimentalResults.dta

. 
. 
. *In the following, we follow the sequence of the prese
> ntation of experimental results in the manuscript
. *We define a binary indicator to perform Fish-Pitman p
> ermutation tests
. gen FPTestIndicator=0 if Treatment=="ControlGroup"
(1,800 missing values generated)

. replace FPTestIndicator=1 if Treatment=="TreatmentGrou
> p"
(1,800 real changes made)

. 
. 
. 
. 
. //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> /////////    Main Data Analysis of Section "Expert Vot
> ers"    ////////
> //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> preserve

. *First, we calculate the quality of democratic choice 
> in each election period
. gen RightChoice=0 if Expertise==1&Vote!=State&Willingn
> ess2Vote>=RandVotingCost
(3,591 missing values generated)

. replace RightChoice=1 if Vote==State&Expertise==1&Will
> ingness2Vote>=RandVotingCost
(760 real changes made)

. gen WrongChoice=0 if Expertise==1&Vote==State&Willingn
> ess2Vote>=RandVotingCost
(2,840 missing values generated)

. replace WrongChoice=1 if Vote!=State&Vote<3&Expertise=
> =1&Willingness2Vote>=RandVotingCost
(9 real changes made)

. 
. by ElectionID, sort: egen NRightChoice=total(RightChoi
> ce)

. by ElectionID, sort: egen NWrongChoice=total(WrongChoi
> ce)

. 
. gen SumRightVotes=NRightChoice+2 if Supportive==1
(2,435 missing values generated)

. replace SumRightVotes=NRightChoice+1 if Neutral==1
(1,180 real changes made)

. replace SumRightVotes=NRightChoice if Against==1
(1,255 real changes made)

. gen SumWrongVotes=NWrongChoice+2 if Against==1
(2,345 missing values generated)

. replace SumWrongVotes=NWrongChoice+1 if Neutral==1
(1,180 real changes made)

. replace SumWrongVotes=NWrongChoice if Supportive==1
(1,165 real changes made)

. 
. gen ProbRight=1 if SumRightVotes>SumWrongVotes
(1,395 missing values generated)

. replace ProbRight=0 if SumRightVotes<SumWrongVotes
(760 real changes made)

. replace ProbRight=0.5 if SumRightVotes==SumWrongVotes
(635 real changes made)

. 
. sort ElectionID

. by ElectionID: gen Quality=ProbRight if _n==1
(2,880 missing values generated)

. 
. *Then, we use electorate verages as the unit of observ
> ation, 
. *leaving us with 12 independent electorates for each t
> reatment group 
. sort ElectorateID

. by ElectorateID: egen AverageQuality=mean(Quality)

. by ElectorateID: gen AQuality=AverageQuality if _n==1
(3,576 missing values generated)

. 
. *Check the electorate averages of the quality of democ
> ratic choice by treatment
. mean AQuality if Treatment=="ControlGroup"

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ------
             |       Mean   Std. Err.     [95% Conf. Int
> erval]
-------------+------------------------------------------
> ------
    AQuality |   .7611111   .0319362        .69082    .8
> 314022
--------------------------------------------------------
> ------

. mean AQuality if Treatment=="TreatmentGroup"

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ------
             |       Mean   Std. Err.     [95% Conf. Int
> erval]
-------------+------------------------------------------
> ------
    AQuality |   .6402778   .0362057      .5605896    .7
> 199659
--------------------------------------------------------
> ------

. 
. *Perform t-test, Mann-Whitney ranksum tests, and Fishe
> r-Pitman permutation tests
. ttest AQuality,by(Treatment)

Two-sample t test with equal variances
--------------------------------------------------------
> ----------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev. 
>   [95% Conf. Interval]
---------+----------------------------------------------
> ----------------------
ControlG |      12    .7611111    .0319362    .1106303  
>     .69082                                            
>               .8314022
Treatmen |      12    .6402778    .0362057    .1254202  
>   .5605896                                            
>               .7199659
---------+----------------------------------------------
> ----------------------
combined |      24    .7006944    .0267593    .1310934  
>   .6453385                                            
>               .7560503
---------+----------------------------------------------
> ----------------------
    diff |            .1208333    .0482781              
>   .0207107                                            
>               .2209559
--------------------------------------------------------
> ----------------------
    diff = mean(ControlG) - mean(Treatmen)              
>           t =   2.5029
Ho: diff = 0                                     degrees
>  of freedom =       22

    Ha: diff < 0                 Ha: diff != 0          
>        Ha: diff > 0
 Pr(T < t) = 0.9899         Pr(|T| > |t|) = 0.0202      
>     Pr(T > t) = 0.0101

. ranksum AQuality,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
ControlGroup |       12         190         150
TreatmentGro |       12         110         150
-------------+---------------------------------
    combined |       24         300         300

unadjusted variance      300.00
adjustment for ties       -0.52
                     ----------
adjusted variance        299.48

Ho: AQuality(Treatm~t==ControlGroup) = AQuality(Treatm~t
> ==TreatmentGroup)
             z =   2.311
    Prob > |z| =   0.0208

. permtest2 AQuality,by(FPTestIndicator)
Fisher-Pitman permutation test for two independent sampl
> es


FPTestIndi~r |      obs        mean    std.dev.
-------------+---------------------------------
           0 |       12   .76111111   .11063027
           1 |       12   .64027778   .12542016
-------------+---------------------------------
    combined |       24   .70069444   .13109343


mode of operation:  Montecarlo simulation (200000 runs)

Progress:  |........................................|

Test of hypothesis Ho: AQuality(FPTestIndicator==0) >= A
> Quality(FPTestIndicator==1) :  p=.98936 (one-tailed)
Test of hypothesis Ho: AQuality(FPTestIndicator==0) <= A
> Quality(FPTestIndicator==1) :  p=.01148 (one-tailed)
Test of hypothesis Ho: AQuality(FPTestIndicator==0) == A
> Quality(FPTestIndicator==1) :  p=.02296 (two-tailed)

. restore

. 
. 
. 
. //////////////////////////////////////////////////////
> ////////////////////
> //////    Examine the average Willingness to vote by t
> reatment     ///////
> //////////////////////////////////////////////////////
> ////////////////////
> 
. preserve

. *In this section, we focus on the analysis of expert v
> oters' willingness to vote
. *As reported later, non-expert voters' in most cases d
> o not vote. 
. *Non-expert voters' willingness to vote is close to ze
> ro.
. drop if Expertise==0 
(1,089 observations deleted)

. *We use the subject level averages of willingness to v
> ote
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTV=mean(Willingnes
> s2Vote)

. by GlobalSubjectID, sort: gen AVotingCutOff=MeanWTV if
>  _n==1
(2,391 missing values generated)

. 
. mean AVotingCutOff if Treatment=="ControlGroup"

Mean estimation                   Number of obs   =     
>     60

--------------------------------------------------------
> -------
              |       Mean   Std. Err.     [95% Conf. In
> terval]
--------------+-----------------------------------------
> -------
AVotingCutOff |   40.28241   2.384594      35.51085    4
> 5.05397
--------------------------------------------------------
> -------

. mean AVotingCutOff if Treatment=="TreatmentGroup"

Mean estimation                   Number of obs   =     
>     60

--------------------------------------------------------
> -------
              |       Mean   Std. Err.     [95% Conf. In
> terval]
--------------+-----------------------------------------
> -------
AVotingCutOff |   24.94893   1.754759      21.43766    2
> 8.46019
--------------------------------------------------------
> -------

. 
. ttest AVotingCutOff,by(Treatment)

Two-sample t test with equal variances
--------------------------------------------------------
> ----------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev. 
>   [95% Conf. Interval]
---------+----------------------------------------------
> ----------------------
ControlG |      60    40.28241    2.384594    18.47098  
>   35.51085                                            
>               45.05397
Treatmen |      60    24.94893    1.754759    13.59231  
>   21.43766                                            
>               28.46019
---------+----------------------------------------------
> ----------------------
combined |     120    32.61567    1.633062     17.8893  
>   29.38204                                            
>               35.84929
---------+----------------------------------------------
> ----------------------
    diff |            15.33348    2.960653              
>   9.470583                                            
>               21.19638
--------------------------------------------------------
> ----------------------
    diff = mean(ControlG) - mean(Treatmen)              
>           t =   5.1791
Ho: diff = 0                                     degrees
>  of freedom =      118

    Ha: diff < 0                 Ha: diff != 0          
>        Ha: diff > 0
 Pr(T < t) = 1.0000         Pr(|T| > |t|) = 0.0000      
>     Pr(T > t) = 0.0000

. ranksum AVotingCutOff,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
ControlGroup |       60      4550.5        3630
TreatmentGro |       60      2709.5        3630
-------------+---------------------------------
    combined |      120        7260        7260

unadjusted variance    36300.00
adjustment for ties       -0.13
                     ----------
adjusted variance      36299.87

Ho: AVotin~f(Treatm~t==ControlGroup) = AVotin~f(Treatm~t
> ==TreatmentGroup)
             z =   4.831
    Prob > |z| =   0.0000

. permtest2 AVotingCutOff,by(FPTestIndicator)
Fisher-Pitman permutation test for two independent sampl
> es


FPTestIndi~r |      obs        mean    std.dev.
-------------+---------------------------------
           0 |       60   40.282408   18.470984
           1 |       60   24.948927   13.592306
-------------+---------------------------------
    combined |      120   32.615667   17.889301


mode of operation:  Montecarlo simulation (200000 runs)

Progress:  |........................................|

Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  >= AVotingCutOff(FPTestIndicator==1) :  p=1 (one-tail
> ed)
Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  <= AVotingCutOff(FPTestIndicator==1) :  p=0 (one-tail
> ed)
Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  == AVotingCutOff(FPTestIndicator==1) :  p=0 (two-tail
> ed)

. restore

. 
. 
. //////////////////////////////////////////////////////
> ////////////////////
> ////////////////                Figure 2              
>    /////////////////
> //////////////////////////////////////////////////////
> ////////////////////
> //Based on the information elicted from above, we know
>  expert voters' WTV in the Control is 40.3, in the Tre
> atment is 24.9//
. //Based on the information elicted from Stata do code 
> Line193 (below), we know non-expert voters' WTV in the
>  Control is 2.0, in the Treatment is 1.3//  
. //Thenn, we report both expert and non-expert voters' 
> WTV together and make Figure 2 using the following cod
> es//
. preserve

. clear

. import excel "D:\FiguresReplications.xlsx",  sheet("Fi
> gure2Expert") firstrow

. twoway (bar Mean Position if Treatment=="ControlGroup"
> ,  name(ExpertWTV,replace) fcolor(gs6) bcolor(gs4) lwi
> dth(0.4) xaxis(1 2) yaxis(1 2) )||(bar Mean Position i
> f Treatment=="TreatmentGroup",  fcolor(gs14) bcolor(gs
> 4) lwidth(0.4)  )||(rcap CI95L CI95H Position,lcolor(g
> s4)  yaxis(1) lwidth(0.4)),  ylabel(0 (10) 60,nogrid) 
> ylabel("",axis(2)) xlabel("") xlabel("",axis(2)) ytitl
> e("Willingness to vote",size(large)) ytitle("",axis(2)
> ) xtitle("") xtitle("",axis(2))     legend(region(lcol
> or(white))  order(1 2 3) ring(0) position(1) symxsize(
> Medium) keygap(tiny)  row(3) label(1 "Control") label(
> 2 "Treatment") label(3 "95% CI")) title("Expert Voters
> ",color(black))  graphregion(color(white)) plotregion(
> color(white))  text(5.5 1 "40.3",place(c) size(huge) c
> olor(black)) text(5.5 2 "24.9",place(c) size(huge) col
> or(black))  
(note:  named style Medium not found in class gsize,
    default attributes used)

. clear

. import excel "D:\FiguresReplications.xlsx",  sheet("Fi
> gure2NonExpert") firstrow

. twoway (bar Mean Position if Treatment=="ControlGroup"
> ,  name(NonExpertWTV,replace) fcolor(gs6) bcolor(gs4) 
> lwidth(0.4) xaxis(1 2) yaxis(1 2) )||(bar Mean Positio
> n if Treatment=="TreatmentGroup",  fcolor(gs14) bcolor
> (gs4) lwidth(0.4)  )||(rcap CI95L CI95H Position,lcolo
> r(gs4)  yaxis(1) lwidth(0.4)),  ylabel(0 (10) 60,nogri
> d) ylabel("",axis(2)) xlabel("") xlabel("",axis(2)) yt
> itle("Willingness to vote",size(large)) ytitle("",axis
> (2)) xtitle("") xtitle("",axis(2))     legend(region(l
> color(white))  order(1 2 3) ring(0) position(1) symxsi
> ze(Medium) keygap(tiny)  row(3) label(1 "Control") lab
> el(2 "Treatment") label(3 "95% CI")) title("Non-Expert
>  Voters",color(black))  graphregion(color(white)) plot
> region(color(white))  text(5.5 1 "2.0",place(c) size(h
> uge) color(black)) text(5.5 2 "1.3",place(c) size(huge
> ) color(black))  
(note:  named style Medium not found in class gsize,
    default attributes used)

. graph combine ExpertWTV NonExpertWTV, name(Figure2,rep
> lace) col(2) graphregion(color(white)) plotregion(colo
> r(white)) note("Note: We average (non)expert voters' w
> illingness to vote and use electorate level averages a
> s the unit of" "independent observation in the statist
> ical analysis.",span)
(note:  named style Medium not found in class gsize,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)

. graph export "D:\Figure2.pdf", as(pdf) replace
(file D:\Figure2.pdf written in PDF format)

. restore

. 
. 
. 
. //////////////////////////////////////////////////////
> ////////////////////
> //Examine the average Willingness to vote by treatment
>  and partisan bias//
. //////////////////////////////////////////////////////
> ////////////////////
> 
. *When partisan bias is against
. mean Willingness2Vote if Treatment=="ControlGroup"&Exp
> ertise==1&Against==1

Mean estimation                   Number of obs   =     
>    463

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |     51.527   1.630356      48.32316  
>   54.73083
--------------------------------------------------------
> ----------

. mean Willingness2Vote if Treatment=="TreatmentGroup"&E
> xpertise==1&Against==1

Mean estimation                   Number of obs   =     
>    422

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   32.35071   1.320294      29.75552  
>    34.9459
--------------------------------------------------------
> ----------

. preserve

. drop if Expertise==0
(1,089 observations deleted)

. drop if Against!=1
(1,626 observations deleted)

. mean Willingness2Vote if Treatment=="ControlGroup"

Mean estimation                   Number of obs   =     
>    463

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |     51.527   1.630356      48.32316  
>   54.73083
--------------------------------------------------------
> ----------

. mean Willingness2Vote if Treatment=="TreatmentGroup"

Mean estimation                   Number of obs   =     
>    422

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   32.35071   1.320294      29.75552  
>    34.9459
--------------------------------------------------------
> ----------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTV=mean(Willingnes
> s2Vote)

. by GlobalSubjectID, sort: gen AVotingCutOff=MeanWTV if
>  _n==1
(765 missing values generated)

. 
. ranksum AVotingCutOff,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
ControlGroup |       60        4465        3630
TreatmentGro |       60        2795        3630
-------------+---------------------------------
    combined |      120        7260        7260

unadjusted variance    36300.00
adjustment for ties       -2.65
                     ----------
adjusted variance      36297.35

Ho: AVotin~f(Treatm~t==ControlGroup) = AVotin~f(Treatm~t
> ==TreatmentGroup)
             z =   4.383
    Prob > |z| =   0.0000

. permtest2 AVotingCutOff,by(FPTestIndicator)
Fisher-Pitman permutation test for two independent sampl
> es


FPTestIndi~r |      obs        mean    std.dev.
-------------+---------------------------------
           0 |       60   51.845493   23.957607
           1 |       60   33.166317   19.388478
-------------+---------------------------------
    combined |      120   42.505905   23.641274


mode of operation:  Montecarlo simulation (200000 runs)

Progress:  |........................................|

Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  >= AVotingCutOff(FPTestIndicator==1) :  p=.999995 (on
> e-tailed)
Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  <= AVotingCutOff(FPTestIndicator==1) :  p=5.000e-06 (
> one-tailed)
Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  == AVotingCutOff(FPTestIndicator==1) :  p=.00001 (two
> -tailed)

. restore

. 
. 
. 
. *When partisan bias is neutral
. mean Willingness2Vote if Treatment=="ControlGroup"&Exp
> ertise==1&Neutral==1

Mean estimation                   Number of obs   =     
>    392

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |    46.3699   1.483668      43.45293  
>   49.28686
--------------------------------------------------------
> ----------

. mean Willingness2Vote if Treatment=="TreatmentGroup"&E
> xpertise==1&Neutral==1

Mean estimation                   Number of obs   =     
>    426

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   28.45305    1.11643      26.25864  
>   30.64746
--------------------------------------------------------
> ----------

. preserve

. drop if Expertise==0
(1,089 observations deleted)

. drop if Neutral!=1
(1,693 observations deleted)

. mean Willingness2Vote if Treatment=="ControlGroup"

Mean estimation                   Number of obs   =     
>    392

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |    46.3699   1.483668      43.45293  
>   49.28686
--------------------------------------------------------
> ----------

. mean Willingness2Vote if Treatment=="TreatmentGroup"

Mean estimation                   Number of obs   =     
>    426

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   28.45305    1.11643      26.25864  
>   30.64746
--------------------------------------------------------
> ----------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTV=mean(Willingnes
> s2Vote)

. by GlobalSubjectID, sort: gen AVotingCutOff=MeanWTV if
>  _n==1
(698 missing values generated)

. 
. ranksum AVotingCutOff,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
ControlGroup |       60        4485        3630
TreatmentGro |       60        2775        3630
-------------+---------------------------------
    combined |      120        7260        7260

unadjusted variance    36300.00
adjustment for ties       -3.66
                     ----------
adjusted variance      36296.34

Ho: AVotin~f(Treatm~t==ControlGroup) = AVotin~f(Treatm~t
> ==TreatmentGroup)
             z =   4.488
    Prob > |z| =   0.0000

. permtest2 AVotingCutOff,by(FPTestIndicator)
Fisher-Pitman permutation test for two independent sampl
> es


FPTestIndi~r |      obs        mean    std.dev.
-------------+---------------------------------
           0 |       60   47.429768    25.83547
           1 |       60   28.191164   15.068936
-------------+---------------------------------
    combined |      120   37.810466   23.169422


mode of operation:  Montecarlo simulation (200000 runs)

Progress:  |........................................|

Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  >= AVotingCutOff(FPTestIndicator==1) :  p=.999995 (on
> e-tailed)
Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  <= AVotingCutOff(FPTestIndicator==1) :  p=5.000e-06 (
> one-tailed)
Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  == AVotingCutOff(FPTestIndicator==1) :  p=.00001 (two
> -tailed)

. restore

. 
. 
. 
. *When partisan bias is supportive
. mean Willingness2Vote if Treatment=="ControlGroup"&Exp
> ertise==1&Supportive==1

Mean estimation                   Number of obs   =     
>    396

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   21.28788   1.436463      18.46381  
>   24.11195
--------------------------------------------------------
> ----------

. mean Willingness2Vote if Treatment=="TreatmentGroup"&E
> xpertise==1&Supportive==1

Mean estimation                   Number of obs   =     
>    412

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   13.64806   1.067955      11.54872  
>   15.74739
--------------------------------------------------------
> ----------

. preserve

. drop if Expertise==0
(1,089 observations deleted)

. drop if Supportive!=1
(1,703 observations deleted)

. mean Willingness2Vote if Treatment=="ControlGroup"

Mean estimation                   Number of obs   =     
>    396

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   21.28788   1.436463      18.46381  
>   24.11195
--------------------------------------------------------
> ----------

. mean Willingness2Vote if Treatment=="TreatmentGroup"

Mean estimation                   Number of obs   =     
>    412

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   13.64806   1.067955      11.54872  
>   15.74739
--------------------------------------------------------
> ----------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTV=mean(Willingnes
> s2Vote)

. by GlobalSubjectID, sort: gen AVotingCutOff=MeanWTV if
>  _n==1
(688 missing values generated)

. 
. ranksum AVotingCutOff,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
ControlGroup |       60      3946.5        3630
TreatmentGro |       60      3313.5        3630
-------------+---------------------------------
    combined |      120        7260        7260

unadjusted variance    36300.00
adjustment for ties     -257.02
                     ----------
adjusted variance      36042.98

Ho: AVotin~f(Treatm~t==ControlGroup) = AVotin~f(Treatm~t
> ==TreatmentGroup)
             z =   1.667
    Prob > |z| =   0.0955

. permtest2 AVotingCutOff,by(FPTestIndicator)
Fisher-Pitman permutation test for two independent sampl
> es


FPTestIndi~r |      obs        mean    std.dev.
-------------+---------------------------------
           0 |       60   21.913669   22.798907
           1 |       60   13.893737   15.785456
-------------+---------------------------------
    combined |      120   17.903703   19.936634


mode of operation:  Montecarlo simulation (200000 runs)

Progress:  |........................................|

Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  >= AVotingCutOff(FPTestIndicator==1) :  p=.98676 (one
> -tailed)
Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  <= AVotingCutOff(FPTestIndicator==1) :  p=.01324 (one
> -tailed)
Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  == AVotingCutOff(FPTestIndicator==1) :  p=.02648 (two
> -tailed)

. restore

. 
. 
. 
. //////////////////////////////////////////////////////
> ////////////////////
> ////////////////                Figure 3              
>    /////////////////
> //////////////////////////////////////////////////////
> ////////////////////
> //Start from Line 168, end at Line 378//
. preserve

. //We elicit expert voters' WTV of the Treatment Group 
> by the number of realized expert voters and partisan b
> ias using the following codes//
. //The mean and corresponding confidence intervals are 
> manually clustered at the subject level//
. drop if Expertise==0
(1,089 observations deleted)

. drop if Treatment=="ControlGroup"
(1,251 observations deleted)

. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVSupportive1=mean
> (Willingness2Vote) if Supportive==1&HowManyHaveExperti
> se==1
(1258 missing values generated)

. by GlobalSubjectID, sort: egen AvergesSupportive1=mean
> (MeanWTVSupportive1)
(1238 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffSupportive1
> =AvergesSupportive1 if _n==1
(1,259 missing values generated)

. mean AVotingCutOffSupportive1

Mean estimation                   Number of obs   =     
>      1

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive1 |       37.5          .        
>      .                                                
>                  .
--------------------------------------------------------
> ------------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVSupportive2=mean
> (Willingness2Vote) if Supportive==1&HowManyHaveExperti
> se==2
(1230 missing values generated)

. by GlobalSubjectID, sort: egen AvergesSupportive2=mean
> (MeanWTVSupportive2)
(743 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffSupportive2
> =AvergesSupportive2 if _n==1
(1,236 missing values generated)

. mean AVotingCutOffSupportive2

Mean estimation                   Number of obs   =     
>     24

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive2 |   12.01042   3.260104      5.
> 266377                                                
>           18.75446
--------------------------------------------------------
> ------------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVSupportive3=mean
> (Willingness2Vote) if Supportive==1&HowManyHaveExperti
> se==3
(1125 missing values generated)

. by GlobalSubjectID, sort: egen AvergesSupportive3=mean
> (MeanWTVSupportive3)
(87 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffSupportive3
> =AvergesSupportive3 if _n==1
(1,204 missing values generated)

. mean AVotingCutOffSupportive3

Mean estimation                   Number of obs   =     
>     56

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive3 |   15.95268   2.954293      10
> .03214                                                
>           21.87321
--------------------------------------------------------
> ------------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVSupportive4=mean
> (Willingness2Vote) if Supportive==1&HowManyHaveExperti
> se==4
(1120 missing values generated)

. by GlobalSubjectID, sort: egen AvergesSupportive4=mean
> (MeanWTVSupportive4)
(40 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffSupportive4
> =AvergesSupportive4 if _n==1
(1,202 missing values generated)

. mean AVotingCutOffSupportive4

Mean estimation                   Number of obs   =     
>     58

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive4 |   11.87471   2.000053      7.
> 869675                                                
>           15.87975
--------------------------------------------------------
> ------------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVSupportive5=mean
> (Willingness2Vote) if Supportive==1&HowManyHaveExperti
> se==5
(1155 missing values generated)

. by GlobalSubjectID, sort: egen AvergesSupportive5=mean
> (MeanWTVSupportive5)
(103 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffSupportive5
> =AvergesSupportive5 if _n==1
(1,205 missing values generated)

. mean AVotingCutOffSupportive5

Mean estimation                   Number of obs   =     
>     55

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive5 |   13.09091   2.885863      7.
> 305102                                                
>           18.87672
--------------------------------------------------------
> ------------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVNeutral1=mean(Wi
> llingness2Vote) if Neutral==1&HowManyHaveExpertise==1
(1257 missing values generated)

. by GlobalSubjectID, sort: egen AvergesNeutral1=mean(Me
> anWTVNeutral1)
(1209 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffNeutral1=Av
> ergesNeutral1 if _n==1
(1,257 missing values generated)

. mean AVotingCutOffNeutral1

Mean estimation                   Number of obs   =     
>      3

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral1 |   23.33333   14.52966     -39.18
> 276                                                   
>        85.84943
--------------------------------------------------------
> ---------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVNeutral2=mean(Wi
> llingness2Vote) if Neutral==1&HowManyHaveExpertise==2
(1232 missing values generated)

. by GlobalSubjectID, sort: egen AvergesNeutral2=mean(Me
> anWTVNeutral2)
(752 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffNeutral2=Av
> ergesNeutral2 if _n==1
(1,236 missing values generated)

. mean AVotingCutOffNeutral2

Mean estimation                   Number of obs   =     
>     24

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral2 |    29.3125   4.672597       19.6
> 465                                                   
>         38.9785
--------------------------------------------------------
> ---------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVNeutral3=mean(Wi
> llingness2Vote) if Neutral==1&HowManyHaveExpertise==3
(1146 missing values generated)

. by GlobalSubjectID, sort: egen AvergesNeutral3=mean(Me
> anWTVNeutral3)
(112 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffNeutral3=Av
> ergesNeutral3 if _n==1
(1,205 missing values generated)

. mean AVotingCutOffNeutral3

Mean estimation                   Number of obs   =     
>     55

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral3 |   27.88758   2.542893      22.78
> 938                                                   
>        32.98577
--------------------------------------------------------
> ---------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVNeutral4=mean(Wi
> llingness2Vote) if Neutral==1&HowManyHaveExpertise==4
(1084 missing values generated)

. by GlobalSubjectID, sort: egen AvergesNeutral4=mean(Me
> anWTVNeutral4)
(52 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffNeutral4=Av
> ergesNeutral4 if _n==1
(1,203 missing values generated)

. mean AVotingCutOffNeutral4

Mean estimation                   Number of obs   =     
>     57

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral4 |   29.10614   2.451269      24.19
> 566                                                   
>        34.01662
--------------------------------------------------------
> ---------------

. 
. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVNeutral5=mean(Wi
> llingness2Vote) if Neutral==1&HowManyHaveExpertise==5
(1155 missing values generated)

. by GlobalSubjectID, sort: egen AvergesNeutral5=mean(Me
> anWTVNeutral5)
(207 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffNeutral5=Av
> ergesNeutral5 if _n==1
(1,210 missing values generated)

. mean AVotingCutOffNeutral5

Mean estimation                   Number of obs   =     
>     50

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral5 |      28.63   3.124501      22.35
> 108                                                   
>        34.90892
--------------------------------------------------------
> ---------------

. 
. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVAgainst1=mean(Wi
> llingness2Vote) if Against==1&HowManyHaveExpertise==1
(1256 missing values generated)

. by GlobalSubjectID, sort: egen AvergesAgainst1=mean(Me
> anWTVAgainst1)
(1172 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffAgainst1=Av
> ergesAgainst1 if _n==1
(1,256 missing values generated)

. mean AVotingCutOffAgainst1

Mean estimation                   Number of obs   =     
>      4

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst1 |          5   3.535534     -6.251
> 647                                                   
>        16.25165
--------------------------------------------------------
> ---------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVAgainst2=mean(Wi
> llingness2Vote) if Against==1&HowManyHaveExpertise==2
(1234 missing values generated)

. by GlobalSubjectID, sort: egen AvergesAgainst2=mean(Me
> anWTVAgainst2)
(813 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffAgainst2=Av
> ergesAgainst2 if _n==1
(1,239 missing values generated)

. mean AVotingCutOffAgainst2

Mean estimation                   Number of obs   =     
>     21

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst2 |   26.21429   5.451362      14.84
> 294                                                   
>        37.58563
--------------------------------------------------------
> ---------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVAgainst3=mean(Wi
> llingness2Vote) if Against==1&HowManyHaveExpertise==3
(1140 missing values generated)

. by GlobalSubjectID, sort: egen AvergesAgainst3=mean(Me
> anWTVAgainst3)
(271 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffAgainst3=Av
> ergesAgainst3 if _n==1
(1,213 missing values generated)

. mean AVotingCutOffAgainst3

Mean estimation                   Number of obs   =     
>     47

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst3 |   33.46277   3.238538      26.94
> 393                                                   
>        39.98161
--------------------------------------------------------
> ---------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVAgainst4=mean(Wi
> llingness2Vote) if Against==1&HowManyHaveExpertise==4
(1048 missing values generated)

. by GlobalSubjectID, sort: egen AvergesAgainst4=mean(Me
> anWTVAgainst4)
(14 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffAgainst4=Av
> ergesAgainst4 if _n==1
(1,201 missing values generated)

. mean AVotingCutOffAgainst4

Mean estimation                   Number of obs   =     
>     59

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst4 |   34.81186   2.766585      29.27
> 394                                                   
>        40.34979
--------------------------------------------------------
> ---------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVAgainst5=mean(Wi
> llingness2Vote) if Against==1&HowManyHaveExpertise==5
(1200 missing values generated)

. by GlobalSubjectID, sort: egen AvergesAgainst5=mean(Me
> anWTVAgainst5)
(416 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffAgainst5=Av
> ergesAgainst5 if _n==1
(1,220 missing values generated)

. mean AVotingCutOffAgainst5

Mean estimation                   Number of obs   =     
>     40

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst5 |    29.6875    4.07414      21.44
> 677                                                   
>        37.92823
--------------------------------------------------------
> ---------------

. restore

. 
. 
. preserve

. //We elicit expert voters' WTV of the Control Group by
>  the number of realized expert voters and partisan bia
> s using the following codes//
. //The mean and corresponding confidence intervals are 
> manually clustered at the subject level//
. 
. drop if Expertise==0
(1,089 observations deleted)

. drop if Treatment=="TreatmentGroup"
(1,260 observations deleted)

. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVSupportive1=mean
> (Willingness2Vote) if Supportive==1&HowManyHaveExperti
> se==1
(1246 missing values generated)

. by GlobalSubjectID, sort: egen AvergesSupportive1=mean
> (MeanWTVSupportive1)
(1143 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffSupportive1
> =AvergesSupportive1 if _n==1
(1,246 missing values generated)

. mean AVotingCutOffSupportive1

Mean estimation                   Number of obs   =     
>      5

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive1 |         14   6.204837     -3.
> 227389                                                
>           31.22739
--------------------------------------------------------
> ------------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVSupportive2=mean
> (Willingness2Vote) if Supportive==1&HowManyHaveExperti
> se==2
(1225 missing values generated)

. by GlobalSubjectID, sort: egen AvergesSupportive2=mean
> (MeanWTVSupportive2)
(814 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffSupportive2
> =AvergesSupportive2 if _n==1
(1,230 missing values generated)

. mean AVotingCutOffSupportive2

Mean estimation                   Number of obs   =     
>     21

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive2 |   24.07143   5.937601      11
> .68581                                                
>           36.45705
--------------------------------------------------------
> ------------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVSupportive3=mean
> (Willingness2Vote) if Supportive==1&HowManyHaveExperti
> se==3
(1125 missing values generated)

. by GlobalSubjectID, sort: egen AvergesSupportive3=mean
> (MeanWTVSupportive3)
(159 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffSupportive3
> =AvergesSupportive3 if _n==1
(1,199 missing values generated)

. mean AVotingCutOffSupportive3

Mean estimation                   Number of obs   =     
>     52

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive3 |   22.02965   3.496741      15
> .00965                                                
>           29.04965
--------------------------------------------------------
> ------------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVSupportive4=mean
> (Willingness2Vote) if Supportive==1&HowManyHaveExperti
> se==4
(1107 missing values generated)

. by GlobalSubjectID, sort: egen AvergesSupportive4=mean
> (MeanWTVSupportive4)
(60 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffSupportive4
> =AvergesSupportive4 if _n==1
(1,194 missing values generated)

. mean AVotingCutOffSupportive4

Mean estimation                   Number of obs   =     
>     57

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive4 |   19.05556   3.219458      12
> .60621                                                
>           25.50491
--------------------------------------------------------
> ------------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVSupportive5=mean
> (Willingness2Vote) if Supportive==1&HowManyHaveExperti
> se==5
(1156 missing values generated)

. by GlobalSubjectID, sort: egen AvergesSupportive5=mean
> (MeanWTVSupportive5)
(207 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffSupportive5
> =AvergesSupportive5 if _n==1
(1,201 missing values generated)

. mean AVotingCutOffSupportive5

Mean estimation                   Number of obs   =     
>     50

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive5 |   19.79667   3.437453      12
> .88885                                                
>           26.70449
--------------------------------------------------------
> ------------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVNeutral1=mean(Wi
> llingness2Vote) if Neutral==1&HowManyHaveExpertise==1
(1246 missing values generated)

. by GlobalSubjectID, sort: egen AvergesNeutral1=mean(Me
> anWTVNeutral1)
(1144 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffNeutral1=Av
> ergesNeutral1 if _n==1
(1,246 missing values generated)

. mean AVotingCutOffNeutral1

Mean estimation                   Number of obs   =     
>      5

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral1 |         46   11.22497      14.83
> 448                                                   
>        77.16552
--------------------------------------------------------
> ---------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVNeutral2=mean(Wi
> llingness2Vote) if Neutral==1&HowManyHaveExpertise==2
(1217 missing values generated)

. by GlobalSubjectID, sort: egen AvergesNeutral2=mean(Me
> anWTVNeutral2)
(705 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffNeutral2=Av
> ergesNeutral2 if _n==1
(1,225 missing values generated)

. mean AVotingCutOffNeutral2

Mean estimation                   Number of obs   =     
>     26

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral2 |   47.69231   4.715284        37.
> 981                                                   
>        57.40362
--------------------------------------------------------
> ---------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVNeutral3=mean(Wi
> llingness2Vote) if Neutral==1&HowManyHaveExpertise==3
(1140 missing values generated)

. by GlobalSubjectID, sort: egen AvergesNeutral3=mean(Me
> anWTVNeutral3)
(177 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffNeutral3=Av
> ergesNeutral3 if _n==1
(1,200 missing values generated)

. mean AVotingCutOffNeutral3

Mean estimation                   Number of obs   =     
>     51

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral3 |   48.88562   3.549539      41.75
> 616                                                   
>        56.01508
--------------------------------------------------------
> ---------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVNeutral4=mean(Wi
> llingness2Vote) if Neutral==1&HowManyHaveExpertise==4
(1099 missing values generated)

. by GlobalSubjectID, sort: egen AvergesNeutral4=mean(Me
> anWTVNeutral4)
(123 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffNeutral4=Av
> ergesNeutral4 if _n==1
(1,197 missing values generated)

. mean AVotingCutOffNeutral4

Mean estimation                   Number of obs   =     
>     54

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral4 |   45.60648   3.890157      37.80
> 381                                                   
>        53.40915
--------------------------------------------------------
> ---------------

. 
. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVNeutral5=mean(Wi
> llingness2Vote) if Neutral==1&HowManyHaveExpertise==5
(1161 missing values generated)

. by GlobalSubjectID, sort: egen AvergesNeutral5=mean(Me
> anWTVNeutral5)
(309 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffNeutral5=Av
> ergesNeutral5 if _n==1
(1,206 missing values generated)

. mean AVotingCutOffNeutral5

Mean estimation                   Number of obs   =     
>     45

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral5 |   45.74074   4.525187      36.62
> 083                                                   
>        54.86066
--------------------------------------------------------
> ---------------

. 
. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVAgainst1=mean(Wi
> llingness2Vote) if Against==1&HowManyHaveExpertise==1
(1249 missing values generated)

. by GlobalSubjectID, sort: egen AvergesAgainst1=mean(Me
> anWTVAgainst1)
(1208 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffAgainst1=Av
> ergesAgainst1 if _n==1
(1,249 missing values generated)

. mean AVotingCutOffAgainst1

Mean estimation                   Number of obs   =     
>      2

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst1 |         45          5     -18.53
> 102                                                   
>         108.531
--------------------------------------------------------
> ---------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVAgainst2=mean(Wi
> llingness2Vote) if Against==1&HowManyHaveExpertise==2
(1219 missing values generated)

. by GlobalSubjectID, sort: egen AvergesAgainst2=mean(Me
> anWTVAgainst2)
(795 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffAgainst2=Av
> ergesAgainst2 if _n==1
(1,229 missing values generated)

. mean AVotingCutOffAgainst2

Mean estimation                   Number of obs   =     
>     22

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst2 |    51.7197   7.744487      35.61
> 415                                                   
>        67.82524
--------------------------------------------------------
> ---------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVAgainst3=mean(Wi
> llingness2Vote) if Against==1&HowManyHaveExpertise==3
(1137 missing values generated)

. by GlobalSubjectID, sort: egen AvergesAgainst3=mean(Me
> anWTVAgainst3)
(161 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffAgainst3=Av
> ergesAgainst3 if _n==1
(1,199 missing values generated)

. mean AVotingCutOffAgainst3

Mean estimation                   Number of obs   =     
>     52

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst3 |   52.17821   4.212611      43.72
> 104                                                   
>        60.63537
--------------------------------------------------------
> ---------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVAgainst4=mean(Wi
> llingness2Vote) if Against==1&HowManyHaveExpertise==4
(1051 missing values generated)

. by GlobalSubjectID, sort: egen AvergesAgainst4=mean(Me
> anWTVAgainst4)
(17 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffAgainst4=Av
> ergesAgainst4 if _n==1
(1,192 missing values generated)

. mean AVotingCutOffAgainst4

Mean estimation                   Number of obs   =     
>     59

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst4 |   51.76533   3.592511      44.57
> 414                                                   
>        58.95653
--------------------------------------------------------
> ---------------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVAgainst5=mean(Wi
> llingness2Vote) if Against==1&HowManyHaveExpertise==5
(1136 missing values generated)

. by GlobalSubjectID, sort: egen AvergesAgainst5=mean(Me
> anWTVAgainst5)
(98 missing values generated)

. by GlobalSubjectID, sort: gen AVotingCutOffAgainst5=Av
> ergesAgainst5 if _n==1
(1,196 missing values generated)

. mean AVotingCutOffAgainst5

Mean estimation                   Number of obs   =     
>     55

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst5 |   51.02727   3.684357      43.64
> 058                                                   
>        58.41396
--------------------------------------------------------
> ---------------

. restore

. 
. preserve

. //Then, based on the information elicted above, we mak
> e Figure 3 using the following codes//
. clear

. import excel "D:\FiguresReplications.xlsx",  sheet("Fi
> gure3") firstrow

. replace Nexpertise=Nexpertise+0.2 if Group=="Treatment
> "
variable Nexpertise was byte now float
(21 real changes made)

. twoway (rspike High95CI Low95CI Nexpertise if Group=="
> Control"&Partisan=="Supportive",  name(Figure3Supporti
> ve,replace) fcolor(gs10) bcolor(gs10) lwidth(0.4) xaxi
> s(1 2) yaxis(1 2) )||(line Mean Nexpertise if Group=="
> Control"&Partisan=="Supportive",lcolor(gs14) lpattern(
> solid))||(scatter Mean Nexpertise if Group=="Control"&
> Partisan=="Supportive",  mcolor(gs6) msize(vlarge) msy
> mbol(S)  )||(rspike High95CI Low95CI Nexpertise if Gro
> up=="Treatment"&Partisan=="Supportive",lcolor(gs10)  y
> axis(1) lwidth(0.4))||(line Mean Nexpertise if Group==
> "Treatment"&Partisan=="Supportive",lcolor(gs14) lpatte
> rn(dash))||(scatter Mean Nexpertise if Group=="Treatme
> nt"&Partisan=="Supportive",  mcolor(gs6) msize(vlarge)
>  msymbol(C)  ),  ylabel(0 (20) 100,nogrid) ylabel("",a
> xis(2)) xlabel(1.05 "1" 2.05 "2" 3.05 "3" 4.05 "4" 5.0
> 5 "5") xlabel("",axis(2)) ytitle("") ytitle("",axis(2)
> ) xtitle("") xtitle("",axis(2))  title("Supportive",co
> lor(black))   legend(region(lcolor(white))  order(3 6 
> 1) ring(0) position(1) symxsize(Medium) keygap(tiny)  
> row(3) label(3 "Control") label(6 "Treatment") label(1
>  "95% CI")) graphregion(color(white)) plotregion(color
> (white))  
(note:  named style C not found in class symbol,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)

. twoway (rspike High95CI Low95CI Nexpertise if Group=="
> Control"&Partisan=="Neutral",  name(Figure3Neutral,rep
> lace) fcolor(gs10) bcolor(gs10) lwidth(0.4) xaxis(1 2)
>  yaxis(1 2) )||(line Mean Nexpertise if Group=="Contro
> l"&Partisan=="Neutral",lcolor(gs14) lpattern(solid))||
> (scatter Mean Nexpertise if Group=="Control"&Partisan=
> ="Neutral",  mcolor(gs6) msize(vlarge) msymbol(S)  )||
> (rspike High95CI Low95CI Nexpertise if Group=="Treatme
> nt"&Partisan=="Neutral",lcolor(gs10)  yaxis(1) lwidth(
> 0.4))||(line Mean Nexpertise if Group=="Treatment"&Par
> tisan=="Neutral",lcolor(gs14) lpattern(dash))||(scatte
> r Mean Nexpertise if Group=="Treatment"&Partisan=="Neu
> tral",  mcolor(gs6) msize(vlarge) msymbol(C)  ),  ylab
> el(0 (20) 100,nogrid) ylabel("",axis(2)) xlabel(1.05 "
> 1" 2.05 "2" 3.05 "3" 4.05 "4" 5.05 "5") xlabel("",axis
> (2)) ytitle("") ytitle("",axis(2)) xtitle("") xtitle("
> ",axis(2)) title("Neutral",color(black))    legend(reg
> ion(lcolor(white))  order(3 6 1) ring(0) position(1) s
> ymxsize(Medium) keygap(tiny)  row(3) label(3 "Control"
> ) label(6 "Treatment") label(1 "95% CI")) graphregion(
> color(white)) plotregion(color(white))  
(note:  named style C not found in class symbol,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)

. twoway (rspike High95CI Low95CI Nexpertise if Group=="
> Control"&Partisan=="Against",  name(Figure3Against,rep
> lace) fcolor(gs10) bcolor(gs10) lwidth(0.4) xaxis(1 2)
>  yaxis(1 2) )||(line Mean Nexpertise if Group=="Contro
> l"&Partisan=="Against",lcolor(gs14) lpattern(solid))||
> (scatter Mean Nexpertise if Group=="Control"&Partisan=
> ="Against",  mcolor(gs6) msize(vlarge) msymbol(S)  )||
> (rspike High95CI Low95CI Nexpertise if Group=="Treatme
> nt"&Partisan=="Against",lcolor(gs10)  yaxis(1) lwidth(
> 0.4))||(line Mean Nexpertise if Group=="Treatment"&Par
> tisan=="Against",lcolor(gs14) lpattern(dash))||(scatte
> r Mean Nexpertise if Group=="Treatment"&Partisan=="Aga
> inst",  mcolor(gs6) msize(vlarge) msymbol(C)  ),  ylab
> el(0 (20) 100,nogrid) ylabel("",axis(2)) xlabel(1.05 "
> 1" 2.05 "2" 3.05 "3" 4.05 "4" 5.05 "5") xlabel("",axis
> (2)) ytitle("") ytitle("",axis(2)) xtitle("") xtitle("
> ",axis(2)) title("Against",color(black))    legend(reg
> ion(lcolor(white))  order(3 6 1) ring(0) position(1) s
> ymxsize(Medium) keygap(tiny)  row(3) label(3 "Control"
> ) label(6 "Treatment") label(1 "95% CI")) graphregion(
> color(white)) plotregion(color(white))  
(note:  named style C not found in class symbol,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)

. graph combine Figure3Against Figure3Neutral Figure3Sup
> portive, name(Figure3,replace) graphregion(color(white
> )) plotregion(color(white)) row(1) l1("Willingness to 
> Vote") b1("Number of Realized Expert Voters") note("No
> te: In both the Control Group and the Treatment Group,
>  on average about 70% of subjects have expertise in ea
> ch election. There are few observations in" "which the
> re are only one expert voter. For the cases in which t
> here are only one expert voter, the lower bound of 95%
>  CI is restrict at 0 and the upper bound" "of 95% CI i
> s restrict at 100.")
(note:  named style C not found in class symbol,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)
(note:  named style C not found in class symbol,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)
(note:  named style C not found in class symbol,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)

. graph display Figure3, xsize(12) ysize(6)

. graph export "D:\Figure3.pdf", as(pdf) replace
(file D:\Figure3.pdf written in PDF format)

. restore

. 
. //////////////////////////////////////////////////////
> ////////////////////
> ////////////////                Figure 4              
>    /////////////////
> //////////////////////////////////////////////////////
> ////////////////////
> preserve

. //We identify the distribution of expert voters' willi
> ngness to vote by treatment and partisan bias using th
> e following codes//
. tab Willingness2Vote if Expertise==1&Treatment=="Contr
> olGroup"

Willingness |
      2Vote |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |        288       23.02       23.02
          1 |         28        2.24       25.26
          2 |          7        0.56       25.82
          3 |          1        0.08       25.90
          4 |          1        0.08       25.98
          5 |         23        1.84       27.82
          6 |          1        0.08       27.90
          7 |          6        0.48       28.38
          8 |          1        0.08       28.46
          9 |          1        0.08       28.54
         10 |         57        4.56       33.09
         12 |          8        0.64       33.73
         14 |          1        0.08       33.81
         15 |         23        1.84       35.65
         16 |          2        0.16       35.81
         17 |          3        0.24       36.05
         19 |          1        0.08       36.13
         20 |         33        2.64       38.77
         21 |          6        0.48       39.25
         22 |          1        0.08       39.33
         23 |          3        0.24       39.57
         24 |          3        0.24       39.81
         25 |         28        2.24       42.05
         26 |          1        0.08       42.13
         27 |          2        0.16       42.29
         28 |          1        0.08       42.37
         29 |          2        0.16       42.53
         30 |         21        1.68       44.20
         32 |          2        0.16       44.36
         33 |          4        0.32       44.68
         34 |          1        0.08       44.76
         35 |         32        2.56       47.32
         36 |          2        0.16       47.48
         37 |          3        0.24       47.72
         38 |          1        0.08       47.80
         40 |         46        3.68       51.48
         41 |          1        0.08       51.56
         42 |          3        0.24       51.80
         43 |          4        0.32       52.12
         44 |          2        0.16       52.28
         45 |         18        1.44       53.72
         46 |          1        0.08       53.80
         47 |          1        0.08       53.88
         48 |          1        0.08       53.96
         49 |          2        0.16       54.12
         50 |        100        7.99       62.11
         51 |          1        0.08       62.19
         52 |          2        0.16       62.35
         53 |          5        0.40       62.75
         54 |          1        0.08       62.83
         55 |         14        1.12       63.95
         56 |          2        0.16       64.11
         57 |          5        0.40       64.51
         58 |          1        0.08       64.59
         59 |          3        0.24       64.83
         60 |         67        5.36       70.18
         61 |          8        0.64       70.82
         62 |          4        0.32       71.14
         63 |          5        0.40       71.54
         64 |          4        0.32       71.86
         65 |         28        2.24       74.10
         66 |          2        0.16       74.26
         67 |          2        0.16       74.42
         69 |          3        0.24       74.66
         70 |         30        2.40       77.06
         72 |          2        0.16       77.22
         73 |          1        0.08       77.30
         74 |          2        0.16       77.46
         75 |         53        4.24       81.69
         76 |          4        0.32       82.01
         77 |          1        0.08       82.09
         79 |          4        0.32       82.41
         80 |         43        3.44       85.85
         81 |          1        0.08       85.93
         82 |          3        0.24       86.17
         84 |          2        0.16       86.33
         85 |         22        1.76       88.09
         86 |          1        0.08       88.17
         87 |          3        0.24       88.41
         88 |          3        0.24       88.65
         89 |          3        0.24       88.89
         90 |         25        2.00       90.89
         91 |          4        0.32       91.21
         92 |          1        0.08       91.29
         94 |          2        0.16       91.45
         95 |         25        2.00       93.45
         96 |          1        0.08       93.53
         97 |          1        0.08       93.61
         98 |          1        0.08       93.69
        100 |         79        6.31      100.00
------------+-----------------------------------
      Total |      1,251      100.00

. tab Willingness2Vote if Expertise==1&Treatment=="Treat
> mentGroup"

Willingness |
      2Vote |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |        296       23.49       23.49
          1 |         55        4.37       27.86
          2 |         12        0.95       28.81
          3 |          4        0.32       29.13
          4 |          7        0.56       29.68
          5 |         54        4.29       33.97
          7 |          6        0.48       34.44
          8 |          6        0.48       34.92
          9 |          3        0.24       35.16
         10 |         74        5.87       41.03
         11 |          2        0.16       41.19
         12 |          3        0.24       41.43
         13 |          4        0.32       41.75
         15 |         71        5.63       47.38
         16 |          5        0.40       47.78
         17 |          3        0.24       48.02
         18 |          5        0.40       48.41
         19 |          2        0.16       48.57
         20 |         61        4.84       53.41
         21 |          3        0.24       53.65
         22 |          2        0.16       53.81
         23 |          6        0.48       54.29
         24 |          1        0.08       54.37
         25 |        103        8.17       62.54
         26 |          2        0.16       62.70
         27 |          2        0.16       62.86
         28 |          1        0.08       62.94
         29 |          3        0.24       63.17
         30 |         48        3.81       66.98
         31 |          1        0.08       67.06
         32 |          2        0.16       67.22
         33 |         13        1.03       68.25
         34 |          1        0.08       68.33
         35 |         34        2.70       71.03
         36 |          3        0.24       71.27
         37 |          1        0.08       71.35
         38 |          6        0.48       71.83
         39 |          2        0.16       71.98
         40 |         41        3.25       75.24
         42 |          6        0.48       75.71
         43 |          5        0.40       76.11
         45 |         24        1.90       78.02
         46 |          6        0.48       78.49
         48 |          2        0.16       78.65
         49 |          3        0.24       78.89
         50 |        117        9.29       88.17
         51 |          4        0.32       88.49
         53 |          1        0.08       88.57
         54 |          1        0.08       88.65
         55 |         13        1.03       89.68
         56 |          1        0.08       89.76
         58 |          1        0.08       89.84
         60 |         24        1.90       91.75
         62 |          2        0.16       91.90
         64 |          2        0.16       92.06
         65 |         11        0.87       92.94
         66 |          3        0.24       93.17
         67 |          3        0.24       93.41
         68 |          1        0.08       93.49
         69 |          1        0.08       93.57
         70 |          7        0.56       94.13
         74 |          2        0.16       94.29
         75 |         11        0.87       95.16
         77 |          1        0.08       95.24
         78 |          1        0.08       95.32
         80 |          7        0.56       95.87
         85 |          3        0.24       96.11
         88 |          1        0.08       96.19
         89 |          3        0.24       96.43
         90 |         11        0.87       97.30
         94 |          1        0.08       97.38
         97 |          2        0.16       97.54
         98 |          2        0.16       97.70
         99 |          9        0.71       98.41
        100 |         20        1.59      100.00
------------+-----------------------------------
      Total |      1,260      100.00

. tab Willingness2Vote if Expertise==1&Treatment=="Contr
> olGroup"&Supportive==1

Willingness |
      2Vote |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |        144       36.36       36.36
          1 |         16        4.04       40.40
          2 |          5        1.26       41.67
          4 |          1        0.25       41.92
          5 |         18        4.55       46.46
          6 |          1        0.25       46.72
          7 |          6        1.52       48.23
          9 |          1        0.25       48.48
         10 |         30        7.58       56.06
         12 |          2        0.51       56.57
         14 |          1        0.25       56.82
         15 |         15        3.79       60.61
         17 |          3        0.76       61.36
         20 |         19        4.80       66.16
         23 |          3        0.76       66.92
         24 |          2        0.51       67.42
         25 |         21        5.30       72.73
         29 |          1        0.25       72.98
         30 |         10        2.53       75.51
         33 |          1        0.25       75.76
         35 |         11        2.78       78.54
         37 |          2        0.51       79.04
         40 |          3        0.76       79.80
         44 |          1        0.25       80.05
         45 |          1        0.25       80.30
         48 |          1        0.25       80.56
         49 |          2        0.51       81.06
         50 |         26        6.57       87.63
         52 |          1        0.25       87.88
         55 |          2        0.51       88.38
         61 |          3        0.76       89.14
         63 |          1        0.25       89.39
         64 |          1        0.25       89.65
         65 |          2        0.51       90.15
         72 |          1        0.25       90.40
         75 |          9        2.27       92.68
         80 |          1        0.25       92.93
         85 |          4        1.01       93.94
         92 |          1        0.25       94.19
         95 |          4        1.01       95.20
        100 |         19        4.80      100.00
------------+-----------------------------------
      Total |        396      100.00

. tab Willingness2Vote if Expertise==1&Treatment=="Treat
> mentGroup"&Supportive==1

Willingness |
      2Vote |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |        152       36.89       36.89
          1 |         41        9.95       46.84
          2 |          5        1.21       48.06
          4 |          4        0.97       49.03
          5 |         32        7.77       56.80
          7 |          5        1.21       58.01
          8 |          4        0.97       58.98
          9 |          2        0.49       59.47
         10 |         22        5.34       64.81
         11 |          1        0.24       65.05
         12 |          3        0.73       65.78
         13 |          2        0.49       66.26
         15 |         25        6.07       72.33
         16 |          2        0.49       72.82
         17 |          2        0.49       73.30
         18 |          1        0.24       73.54
         19 |          1        0.24       73.79
         20 |         13        3.16       76.94
         21 |          2        0.49       77.43
         22 |          1        0.24       77.67
         23 |          4        0.97       78.64
         25 |         31        7.52       86.17
         26 |          1        0.24       86.41
         27 |          2        0.49       86.89
         30 |          5        1.21       88.11
         33 |          2        0.49       88.59
         35 |          3        0.73       89.32
         37 |          1        0.24       89.56
         40 |          3        0.73       90.29
         45 |          2        0.49       90.78
         50 |         14        3.40       94.17
         55 |          1        0.24       94.42
         60 |          1        0.24       94.66
         65 |          2        0.49       95.15
         70 |          1        0.24       95.39
         74 |          1        0.24       95.63
         75 |          6        1.46       97.09
         85 |          1        0.24       97.33
         90 |          2        0.49       97.82
         99 |          3        0.73       98.54
        100 |          6        1.46      100.00
------------+-----------------------------------
      Total |        412      100.00

. tab Willingness2Vote if Expertise==1&Treatment=="Contr
> olGroup"&Neutral==1

Willingness |
      2Vote |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |         45       11.48       11.48
          1 |          9        2.30       13.78
          2 |          1        0.26       14.03
          3 |          1        0.26       14.29
          5 |          4        1.02       15.31
         10 |         19        4.85       20.15
         12 |          5        1.28       21.43
         15 |          7        1.79       23.21
         16 |          2        0.51       23.72
         20 |         12        3.06       26.79
         25 |          3        0.77       27.55
         26 |          1        0.26       27.81
         30 |          6        1.53       29.34
         32 |          1        0.26       29.59
         34 |          1        0.26       29.85
         35 |         12        3.06       32.91
         36 |          1        0.26       33.16
         37 |          1        0.26       33.42
         40 |         25        6.38       39.80
         41 |          1        0.26       40.05
         42 |          1        0.26       40.31
         43 |          3        0.77       41.07
         44 |          1        0.26       41.33
         45 |         11        2.81       44.13
         46 |          1        0.26       44.39
         47 |          1        0.26       44.64
         50 |         44       11.22       55.87
         52 |          1        0.26       56.12
         53 |          1        0.26       56.38
         55 |          8        2.04       58.42
         56 |          1        0.26       58.67
         57 |          1        0.26       58.93
         59 |          1        0.26       59.18
         60 |         49       12.50       71.68
         62 |          1        0.26       71.94
         63 |          1        0.26       72.19
         64 |          2        0.51       72.70
         65 |         12        3.06       75.77
         67 |          1        0.26       76.02
         69 |          1        0.26       76.28
         70 |          5        1.28       77.55
         75 |         21        5.36       82.91
         76 |          3        0.77       83.67
         79 |          4        1.02       84.69
         80 |         21        5.36       90.05
         82 |          1        0.26       90.31
         85 |          4        1.02       91.33
         86 |          1        0.26       91.58
         87 |          2        0.51       92.09
         88 |          1        0.26       92.35
         89 |          2        0.51       92.86
         90 |          7        1.79       94.64
         94 |          1        0.26       94.90
         95 |          3        0.77       95.66
        100 |         17        4.34      100.00
------------+-----------------------------------
      Total |        392      100.00

. tab Willingness2Vote if Expertise==1&Treatment=="Treat
> mentGroup"&Neutral==1

Willingness |
      2Vote |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |         67       15.73       15.73
          1 |          5        1.17       16.90
          2 |          5        1.17       18.08
          3 |          2        0.47       18.54
          4 |          2        0.47       19.01
          5 |         13        3.05       22.07
          8 |          1        0.23       22.30
          9 |          1        0.23       22.54
         10 |         35        8.22       30.75
         11 |          1        0.23       30.99
         13 |          1        0.23       31.22
         15 |         20        4.69       35.92
         16 |          3        0.70       36.62
         18 |          3        0.70       37.32
         20 |         21        4.93       42.25
         21 |          1        0.23       42.49
         22 |          1        0.23       42.72
         23 |          1        0.23       42.96
         25 |         38        8.92       51.88
         26 |          1        0.23       52.11
         28 |          1        0.23       52.35
         29 |          1        0.23       52.58
         30 |         28        6.57       59.15
         31 |          1        0.23       59.39
         32 |          1        0.23       59.62
         33 |         11        2.58       62.21
         35 |         20        4.69       66.90
         36 |          3        0.70       67.61
         38 |          3        0.70       68.31
         39 |          2        0.47       68.78
         40 |         14        3.29       72.07
         43 |          4        0.94       73.00
         45 |          8        1.88       74.88
         46 |          1        0.23       75.12
         48 |          1        0.23       75.35
         49 |          1        0.23       75.59
         50 |         59       13.85       89.44
         51 |          2        0.47       89.91
         54 |          1        0.23       90.14
         55 |          8        1.88       92.02
         60 |          7        1.64       93.66
         64 |          1        0.23       93.90
         65 |          2        0.47       94.37
         66 |          2        0.47       94.84
         70 |          1        0.23       95.07
         74 |          1        0.23       95.31
         75 |          3        0.70       96.01
         77 |          1        0.23       96.24
         80 |          2        0.47       96.71
         89 |          3        0.70       97.42
         90 |          5        1.17       98.59
         99 |          1        0.23       98.83
        100 |          5        1.17      100.00
------------+-----------------------------------
      Total |        426      100.00

. tab Willingness2Vote if Expertise==1&Treatment=="Contr
> olGroup"&Against==1

Willingness |
      2Vote |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |         99       21.38       21.38
          1 |          3        0.65       22.03
          2 |          1        0.22       22.25
          5 |          1        0.22       22.46
          8 |          1        0.22       22.68
         10 |          8        1.73       24.41
         12 |          1        0.22       24.62
         15 |          1        0.22       24.84
         19 |          1        0.22       25.05
         20 |          2        0.43       25.49
         21 |          6        1.30       26.78
         22 |          1        0.22       27.00
         24 |          1        0.22       27.21
         25 |          4        0.86       28.08
         27 |          2        0.43       28.51
         28 |          1        0.22       28.73
         29 |          1        0.22       28.94
         30 |          5        1.08       30.02
         32 |          1        0.22       30.24
         33 |          3        0.65       30.89
         35 |          9        1.94       32.83
         36 |          1        0.22       33.05
         38 |          1        0.22       33.26
         40 |         18        3.89       37.15
         42 |          2        0.43       37.58
         43 |          1        0.22       37.80
         45 |          6        1.30       39.09
         50 |         30        6.48       45.57
         51 |          1        0.22       45.79
         53 |          4        0.86       46.65
         54 |          1        0.22       46.87
         55 |          4        0.86       47.73
         56 |          1        0.22       47.95
         57 |          4        0.86       48.81
         58 |          1        0.22       49.03
         59 |          2        0.43       49.46
         60 |         18        3.89       53.35
         61 |          5        1.08       54.43
         62 |          3        0.65       55.08
         63 |          3        0.65       55.72
         64 |          1        0.22       55.94
         65 |         14        3.02       58.96
         66 |          2        0.43       59.40
         67 |          1        0.22       59.61
         69 |          2        0.43       60.04
         70 |         25        5.40       65.44
         72 |          1        0.22       65.66
         73 |          1        0.22       65.87
         74 |          2        0.43       66.31
         75 |         23        4.97       71.27
         76 |          1        0.22       71.49
         77 |          1        0.22       71.71
         80 |         21        4.54       76.24
         81 |          1        0.22       76.46
         82 |          2        0.43       76.89
         84 |          2        0.43       77.32
         85 |         14        3.02       80.35
         87 |          1        0.22       80.56
         88 |          2        0.43       80.99
         89 |          1        0.22       81.21
         90 |         18        3.89       85.10
         91 |          4        0.86       85.96
         94 |          1        0.22       86.18
         95 |         18        3.89       90.06
         96 |          1        0.22       90.28
         97 |          1        0.22       90.50
         98 |          1        0.22       90.71
        100 |         43        9.29      100.00
------------+-----------------------------------
      Total |        463      100.00

. tab Willingness2Vote if Expertise==1&Treatment=="Treat
> mentGroup"&Against==1

Willingness |
      2Vote |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |         77       18.25       18.25
          1 |          9        2.13       20.38
          2 |          2        0.47       20.85
          3 |          2        0.47       21.33
          4 |          1        0.24       21.56
          5 |          9        2.13       23.70
          7 |          1        0.24       23.93
          8 |          1        0.24       24.17
         10 |         17        4.03       28.20
         13 |          1        0.24       28.44
         15 |         26        6.16       34.60
         17 |          1        0.24       34.83
         18 |          1        0.24       35.07
         19 |          1        0.24       35.31
         20 |         27        6.40       41.71
         23 |          1        0.24       41.94
         24 |          1        0.24       42.18
         25 |         34        8.06       50.24
         29 |          2        0.47       50.71
         30 |         15        3.55       54.27
         32 |          1        0.24       54.50
         34 |          1        0.24       54.74
         35 |         11        2.61       57.35
         38 |          3        0.71       58.06
         40 |         24        5.69       63.74
         42 |          6        1.42       65.17
         43 |          1        0.24       65.40
         45 |         14        3.32       68.72
         46 |          5        1.18       69.91
         48 |          1        0.24       70.14
         49 |          2        0.47       70.62
         50 |         44       10.43       81.04
         51 |          2        0.47       81.52
         53 |          1        0.24       81.75
         55 |          4        0.95       82.70
         56 |          1        0.24       82.94
         58 |          1        0.24       83.18
         60 |         16        3.79       86.97
         62 |          2        0.47       87.44
         64 |          1        0.24       87.68
         65 |          7        1.66       89.34
         66 |          1        0.24       89.57
         67 |          3        0.71       90.28
         68 |          1        0.24       90.52
         69 |          1        0.24       90.76
         70 |          5        1.18       91.94
         75 |          2        0.47       92.42
         78 |          1        0.24       92.65
         80 |          5        1.18       93.84
         85 |          2        0.47       94.31
         88 |          1        0.24       94.55
         90 |          4        0.95       95.50
         94 |          1        0.24       95.73
         97 |          2        0.47       96.21
         98 |          2        0.47       96.68
         99 |          5        1.18       97.87
        100 |          9        2.13      100.00
------------+-----------------------------------
      Total |        422      100.00

. 
. //Then, based on the information elicted above, we mak
> e Figure 4 using the following codes//
. clear

. import excel "D:\FiguresReplications.xlsx",  sheet("Fi
> gure4") firstrow

. twoway (line CDF WTV if Category=="Control"&Selection=
> ="Pool", name(pooledCDF,replace) lcolor(gs6) lpattern(
> solid) lwidth(thick))||(line CDF WTV if Category=="Tre
> atment"&Selection=="Pool", lcolor(gs10) lpattern(dash)
>  lwidth(thick)),ylabel(0 (25) 100,axis(1) nogrid)  xla
> bel(0 (25) 100,axis(1) nogrid) ytitle("",axis(1))   xt
> itle("",axis(1)) title("Pooled",color(black))   graphr
> egion(color(white)) plotregion(color(white)) legend(re
> gion(lcolor(white))  order(1 2) ring(0) position(5) sy
> mxsize(5) keygap(Medium)  row(1) label(1 "Control Grou
> p") label(2 "Treatment Group")) 
(note:  named style Medium not found in class gsize,
    default attributes used)

. twoway (line CDF WTV if Category=="Control"&Selection=
> ="Against", name(againstCDF,replace) lcolor(gs6) lpatt
> ern(solid) lwidth(thick))||(line CDF WTV if Category==
> "Treatment"&Selection=="Against", lcolor(gs10) lpatter
> n(dash) lwidth(thick)),ylabel(0 (25) 100,axis(1) nogri
> d)  xlabel(0 (25) 100,axis(1) nogrid) ytitle("",axis(1
> ))   xtitle("",axis(1))  title("Against",color(black))
>    graphregion(color(white)) plotregion(color(white)) 
> legend(region(lcolor(white))  order(1 2) ring(0) posit
> ion(5) symxsize(Medium) keygap(Medium)  row(1) label(1
>  "Control Group") label(2 "Treatment Group")) 
(note:  named style Medium not found in class gsize,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)

. twoway (line CDF WTV if Category=="Control"&Selection=
> ="Neutral", name(neutralCDF,replace) lcolor(gs6) lpatt
> ern(solid) lwidth(thick))||(line CDF WTV if Category==
> "Treatment"&Selection=="Neutral", lcolor(gs10) lpatter
> n(dash) lwidth(thick)),ylabel(0 (25) 100,axis(1) nogri
> d)  xlabel(0 (25) 100,axis(1) nogrid) ytitle("",axis(1
> ))   xtitle("",axis(1))  title("Neutral",color(black))
>    graphregion(color(white)) plotregion(color(white)) 
> legend(region(lcolor(white))  order(1 2) ring(0) posit
> ion(5) symxsize(Medium) keygap(Medium)  row(1) label(1
>  "Control Group") label(2 "Treatment Group")) 
(note:  named style Medium not found in class gsize,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)

. twoway (line CDF WTV if Category=="Control"&Selection=
> ="Supportive", name(supportiveCDF,replace) lcolor(gs6)
>  lpattern(solid) lwidth(thick))||(line CDF WTV if Cate
> gory=="Treatment"&Selection=="Supportive", lcolor(gs10
> ) lpattern(dash) lwidth(thick)),ylabel(0 (25) 100,axis
> (1) nogrid)  xlabel(0 (25) 100,axis(1) nogrid) ytitle(
> "",axis(1))   xtitle("",axis(1))  title("Supportive",c
> olor(black))   graphregion(color(white)) plotregion(co
> lor(white)) legend(region(lcolor(white))  order(1 2) r
> ing(0) position(5) symxsize(Medium) keygap(Medium)  ro
> w(1) label(1 "Control Group") label(2 "Treatment Group
> ")) 
(note:  named style Medium not found in class gsize,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)

. grc1leg pooledCDF againstCDF neutralCDF supportiveCDF,
>  name(Figure4,replace) col(2) l1("CDF of Observed Will
> ingness to Vote (%)") b1("Willingness to Vote") graphr
> egion(color(white)) plotregion(color(white))
(note:  named style Medium not found in class gsize,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)

. graph display Figure4,xsize(12) ysize(12)

. graph export "D:\Figure4.pdf", as(pdf) replace
(file D:\Figure4.pdf written in PDF format)

. restore

. 
. 
. 
. 
. 
. 
. 
. 
. //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> /////////   Main Data Analysis of Section "Non-Expert 
> Voters" ////////
> //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> preserve

. *In this section, we focus on the analysis of non-expe
> rt voters' behavior
. drop if Expertise==1
(2,511 observations deleted)

. gen Abstain=0

. replace Abstain=1 if Vote==3
(1,014 real changes made)

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen AbstainX=mean(Abstain)

. by GlobalSubjectID, sort: gen NonExpertAbstain=Abstain
> X if _n==1
(969 missing values generated)

. *The average frequency that non-expert voters abstain
. mean NonExpertAbstain

Mean estimation                   Number of obs   =     
>    120

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
NonExpertAbstain |   .9325524   .0130538      .9067047  
>   .9584002
--------------------------------------------------------
> ----------

. 
. *The average willingness to vote of non-expert voters 
> by treatment
. mean Willingness2Vote if Treatment=="ControlGroup"

Mean estimation                   Number of obs   =     
>    549

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   1.952641   .4310625      1.105904  
>   2.799378
--------------------------------------------------------
> ----------

. mean Willingness2Vote if Treatment=="TreatmentGroup"

Mean estimation                   Number of obs   =     
>    540

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   1.311111   .2608712      .7986623  
>    1.82356
--------------------------------------------------------
> ----------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTV=mean(Willingnes
> s2Vote)

. by GlobalSubjectID, sort: gen AVotingCutOff=MeanWTV if
>  _n==1
(969 missing values generated)

. 
. *Perform t-test, Mann-Whitney ranksum tests, and Fishe
> r-Pitman permutation tests
. ttest AVotingCutOff,by(Treatment)

Two-sample t test with equal variances
--------------------------------------------------------
> ----------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev. 
>   [95% Conf. Interval]
---------+----------------------------------------------
> ----------------------
ControlG |      60     2.01042    .7692538    5.958614  
>   .4711467                                            
>               3.549693
Treatmen |      60    1.291906    .3837881    2.972809  
>   .5239479                                            
>               2.059864
---------+----------------------------------------------
> ----------------------
combined |     120    1.651163    .4292938    4.702678  
>   .8011185                                            
>               2.501208
---------+----------------------------------------------
> ----------------------
    diff |            .7185139    .8596771              
>  -.9838808                                            
>               2.420909
--------------------------------------------------------
> ----------------------
    diff = mean(ControlG) - mean(Treatmen)              
>           t =   0.8358
Ho: diff = 0                                     degrees
>  of freedom =      118

    Ha: diff < 0                 Ha: diff != 0          
>        Ha: diff > 0
 Pr(T < t) = 0.7975         Pr(|T| > |t|) = 0.4050      
>     Pr(T > t) = 0.2025

. ranksum AVotingCutOff,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
ControlGroup |       60        3558        3630
TreatmentGro |       60        3702        3630
-------------+---------------------------------
    combined |      120        7260        7260

unadjusted variance    36300.00
adjustment for ties   -12450.76
                     ----------
adjusted variance      23849.24

Ho: AVotin~f(Treatm~t==ControlGroup) = AVotin~f(Treatm~t
> ==TreatmentGroup)
             z =  -0.466
    Prob > |z| =   0.6411

. permtest2 AVotingCutOff,by(FPTestIndicator)
Fisher-Pitman permutation test for two independent sampl
> es


FPTestIndi~r |      obs        mean    std.dev.
-------------+---------------------------------
           0 |       60   2.0104199   5.9586142
           1 |       60   1.2919061   2.9728095
-------------+---------------------------------
    combined |      120    1.651163   4.7026776


mode of operation:  Montecarlo simulation (200000 runs)

Progress:  |........................................|

Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  >= AVotingCutOff(FPTestIndicator==1) :  p=.77392 (one
> -tailed)
Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  <= AVotingCutOff(FPTestIndicator==1) :  p=.22608 (one
> -tailed)
Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  == AVotingCutOff(FPTestIndicator==1) :  p=.45216 (two
> -tailed)

. 
. gen NonExpertVotingNotCounted=1

. replace NonExpertVotingNotCounted=0 if Willingness2Vot
> e>=RandVotingCost
(18 real changes made)

. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen NotCounted=mean(NonExpe
> rtVotingNotCounted)

. by GlobalSubjectID, sort: gen NonExpertVotesNotCounted
> =NotCounted if _n==1
(969 missing values generated)

. *The average frequency that non-expert voters' ballots
>  were not counted in experiments
. mean NonExpertVotesNotCounted

Mean estimation                   Number of obs   =     
>    120

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
NonExpertVotesNotCounted |   .9829733   .0048247        
> .97342                                                
>           .9925266
--------------------------------------------------------
> ------------------

. restore

. 
. //////////////////////////////////////////////////////
> //////////////////////////////
> //A kind of difference-in-differences analysis of will
> ingness to vote by treatment//
. //////////////////////////////////////////////////////
> //////////////////////////////
> 
. preserve

. *First, generate average willingness to vote of expert
>  voters
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVI=mean(Willingne
> ss2Vote) if Expertise==1
(1089 missing values generated)

. by GlobalSubjectID, sort: egen MeanWTVIX=mean(MeanWTVI
> )

. by GlobalSubjectID, sort: gen AVotingCutOffI=MeanWTVIX
>  if _n==1
(3,480 missing values generated)

. mean AVotingCutOffI if Treatment=="ControlGroup"

Mean estimation                   Number of obs   =     
>     60

--------------------------------------------------------
> --------
               |       Mean   Std. Err.     [95% Conf. I
> nterval]
---------------+----------------------------------------
> --------
AVotingCutOffI |   40.28241   2.384594      35.51085    
> 45.05397
--------------------------------------------------------
> --------

. mean AVotingCutOffI if Treatment=="TreatmentGroup"

Mean estimation                   Number of obs   =     
>     60

--------------------------------------------------------
> --------
               |       Mean   Std. Err.     [95% Conf. I
> nterval]
---------------+----------------------------------------
> --------
AVotingCutOffI |   24.94893   1.754759      21.43766    
> 28.46019
--------------------------------------------------------
> --------

. *Then, generate average willingness to vote of non-exp
> ert voters
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTVUI=mean(Willingn
> ess2Vote) if Expertise==0
(2511 missing values generated)

. by GlobalSubjectID, sort: egen MeanWTVUIX=mean(MeanWTV
> UI)

. by GlobalSubjectID, sort: gen AVotingCutOffUI=MeanWTVU
> IX if _n==1
(3,480 missing values generated)

. mean AVotingCutOffUI if Treatment=="ControlGroup"

Mean estimation                   Number of obs   =     
>     60

--------------------------------------------------------
> ---------
                |       Mean   Std. Err.     [95% Conf. 
> Interval]
----------------+---------------------------------------
> ---------
AVotingCutOffUI |    2.01042   .7692538      .4711467   
>  3.549693
--------------------------------------------------------
> ---------

. mean AVotingCutOffUI if Treatment=="TreatmentGroup"

Mean estimation                   Number of obs   =     
>     60

--------------------------------------------------------
> ---------
                |       Mean   Std. Err.     [95% Conf. 
> Interval]
----------------+---------------------------------------
> ---------
AVotingCutOffUI |   1.291906   .3837881      .5239479   
>  2.059864
--------------------------------------------------------
> ---------

. *Perform Mann-Whitney signrank tests, and Fisher-Pitma
> n permutation tests
. *to examine whether expert-voters' willingness to vote
>  are different from non-expert voters
. signrank AVotingCutOffI=AVotingCutOffUI if Treatment==
> "ControlGroup"

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |       60        1830         915
    negative |        0           0         915
        zero |        0           0           0
-------------+---------------------------------
         all |       60        1830        1830

unadjusted variance    18452.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance      18452.50

Ho: AVotingCutOffI = AVotingCutOffUI 
             z =   6.736
    Prob > |z| =   0.0000

. permtest1 AVotingCutOffI=AVotingCutOffUI if Treatment=
> ="ControlGroup"
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffI-AVotingCutOffUI 
-------------------+---------------------------------
 observations      | 60
  - positive       | 60
  - negative       | 0
  - zero           | 0
-------------------+---------------------------------
  critical value   | 2296.319307491184


mode of operation:  Montecarlo simulation (200000 runs)

Progress:  |........................................|

Test of hypothesis Ho: AVotingCutOffI>=AVotingCutOffUI  
> : p = 1
Test of hypothesis Ho: AVotingCutOffI<=AVotingCutOffUI  
> : p = 0
Test of hypothesis Ho: AVotingCutOffI==AVotingCutOffUI  
> : p = 0

. 
. signrank AVotingCutOffI=AVotingCutOffUI if Treatment==
> "TreatmentGroup"

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |       60        1830         915
    negative |        0           0         915
        zero |        0           0           0
-------------+---------------------------------
         all |       60        1830        1830

unadjusted variance    18452.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance      18452.50

Ho: AVotingCutOffI = AVotingCutOffUI 
             z =   6.736
    Prob > |z| =   0.0000

. permtest1 AVotingCutOffI=AVotingCutOffUI if Treatment=
> ="TreatmentGroup"
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffI-AVotingCutOffUI 
-------------------+---------------------------------
 observations      | 60
  - positive       | 60
  - negative       | 0
  - zero           | 0
-------------------+---------------------------------
  critical value   | 1419.421229362488


mode of operation:  Montecarlo simulation (200000 runs)

Progress:  |........................................|

Test of hypothesis Ho: AVotingCutOffI>=AVotingCutOffUI  
> : p = 1
Test of hypothesis Ho: AVotingCutOffI<=AVotingCutOffUI  
> : p = 0
Test of hypothesis Ho: AVotingCutOffI==AVotingCutOffUI  
> : p = 0

. 
. *Generate subject-level average differences of willing
> ness to vote between being experts and being non-exper
> ts
. gen DiffCutoffVoting=AVotingCutOffI-AVotingCutOffUI
(3,480 missing values generated)

. *Perform t-test, Mann-Whitney ranksum tests, and Fishe
> r-Pitman permutation tests
. *to examine whether the differences are different betw
> een treatments
. ttest DiffCutoffVoting,by(Treatment)

Two-sample t test with equal variances
--------------------------------------------------------
> ----------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev. 
>   [95% Conf. Interval]
---------+----------------------------------------------
> ----------------------
ControlG |      60    38.27199    2.294762    17.77515  
>   33.68018                                            
>                42.8638
Treatmen |      60    23.65702    1.705432    13.21022  
>   20.24446                                            
>               27.06958
---------+----------------------------------------------
> ----------------------
combined |     120     30.9645    1.573267    17.23427  
>   27.84928                                            
>               34.07973
---------+----------------------------------------------
> ----------------------
    diff |            14.61497    2.859096              
>   8.953179                                            
>               20.27676
--------------------------------------------------------
> ----------------------
    diff = mean(ControlG) - mean(Treatmen)              
>           t =   5.1117
Ho: diff = 0                                     degrees
>  of freedom =      118

    Ha: diff < 0                 Ha: diff != 0          
>        Ha: diff > 0
 Pr(T < t) = 1.0000         Pr(|T| > |t|) = 0.0000      
>     Pr(T > t) = 0.0000

. ranksum DiffCutoffVoting,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
ControlGroup |       60      4555.5        3630
TreatmentGro |       60      2704.5        3630
-------------+---------------------------------
    combined |      120        7260        7260

unadjusted variance    36300.00
adjustment for ties       -0.13
                     ----------
adjusted variance      36299.87

Ho: DiffCu~g(Treatm~t==ControlGroup) = DiffCu~g(Treatm~t
> ==TreatmentGroup)
             z =   4.858
    Prob > |z| =   0.0000

. permtest2 DiffCutoffVoting,by(FPTestIndicator)
Fisher-Pitman permutation test for two independent sampl
> es


FPTestIndi~r |      obs        mean    std.dev.
-------------+---------------------------------
           0 |       60   38.271989   17.775153
           1 |       60    23.65702   13.210216
-------------+---------------------------------
    combined |      120   30.964504   17.234274


mode of operation:  Montecarlo simulation (200000 runs)

Progress:  |........................................|

Test of hypothesis Ho: DiffCutoffVoting(FPTestIndicator=
> =0) >= DiffCutoffVoting(FPTestIndicator==1) :  p=1 (on
> e-tailed)
Test of hypothesis Ho: DiffCutoffVoting(FPTestIndicator=
> =0) <= DiffCutoffVoting(FPTestIndicator==1) :  p=0 (on
> e-tailed)
Test of hypothesis Ho: DiffCutoffVoting(FPTestIndicator=
> =0) == DiffCutoffVoting(FPTestIndicator==1) :  p=0 (tw
> o-tailed)

. restore

. 
. 
. 
. //////////////////////////////////////////////////////
> ////////////////////
> ////////////////                Figure 5              
>    /////////////////
> //////////////////////////////////////////////////////
> ////////////////////
> preserve

. //Based on the information elicted above, we make Figu
> re 5 using the following codes//
. clear

. import excel "D:\FiguresReplications.xlsx",  sheet("Fi
> gure5") firstrow

. twoway (bar Mean Position if Treatment=="ControlGroup"
> ,  name(Figure5,replace) fcolor(gs6) bcolor(gs4) lwidt
> h(0.4) xaxis(1 2) yaxis(1 2) )||(bar Mean Position if 
> Treatment=="TreatmentGroup",  fcolor(gs14) bcolor(gs4)
>  lwidth(0.4)  )||(rcap CI95L CI95H Position,lcolor(gs4
> )  yaxis(1) lwidth(0.4)),  ylabel(0 (10) 60,nogrid) yl
> abel("",axis(2)) xlabel("") xlabel("",axis(2)) ytitle(
> "{&Delta} Willingness to vote between Expert and Non-E
> xpert",size(3)) ytitle("",axis(2)) xtitle("") xtitle("
> ",axis(2))     legend(region(lcolor(white))  order(1 2
>  3) ring(0) position(1) symxsize(Medium) keygap(tiny) 
>  row(3) label(1 "Control") label(2 "Treatment") label(
> 3 "95% CI")) graphregion(color(white)) plotregion(colo
> r(white))  text(8 1 "38.3",place(c) size(huge) color(b
> lack)) text(8 2 "23.7",place(c) size(huge) color(black
> ))  note("Note: We average (non)expert voters' willing
> ness to vote and use electorate" "averages as the unit
>  of independent observation in the statistical analysi
> s.",span)
(note:  named style Medium not found in class gsize,
    default attributes used)

. graph display Figure5, xsize(6) ysize(6)

. graph export "D:\Figure5.pdf", as(pdf) replace
(file D:\Figure5.pdf written in PDF format)

. restore

. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> ///////// Main Data Analysis of Section "Maximum Engag
> ement" ////////
> //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> 
. 
. /////////  Calculations of Maximum Engagement in Secti
> on 4.1  ////////
> 
. preserve

. clear

. set obs 1000
number of observations (_N) was 0, now 1,000

. gen rho=_n

. replace rho=rho*0.001
(1,000 real changes made)

. gen Quality=(1/3)*(2-(3/2)*(1-rho)^5-5*rho*(1-rho)^4-(
> 1/2)*10*rho^2*(1-rho)^3)+1/3

. tab Quality if _n==700

    Quality |      Freq.     Percent        Cum.
------------+-----------------------------------
    .967285 |          1      100.00      100.00
------------+-----------------------------------
      Total |          1      100.00

. restore

. 
. //Compare Experimental Quality of Democratic Choice to
>  Max. Enagement Benchmark//
. 
. preserve

. gen RightChoice=0 if Expertise==1&Vote!=State&Willingn
> ess2Vote>=RandVotingCost
(3,591 missing values generated)

. replace RightChoice=1 if Vote==State&Expertise==1&Will
> ingness2Vote>=RandVotingCost
(760 real changes made)

. gen WrongChoice=0 if Expertise==1&Vote==State&Willingn
> ess2Vote>=RandVotingCost
(2,840 missing values generated)

. replace WrongChoice=1 if Vote!=State&Vote<3&Expertise=
> =1&Willingness2Vote>=RandVotingCost
(9 real changes made)

. 
. by ElectionID, sort: egen NRightChoice=total(RightChoi
> ce)

. by ElectionID, sort: egen NWrongChoice=total(WrongChoi
> ce)

. 
. gen SumRightVotes=NRightChoice+2 if Supportive==1
(2,435 missing values generated)

. replace SumRightVotes=NRightChoice+1 if Neutral==1
(1,180 real changes made)

. replace SumRightVotes=NRightChoice if Against==1
(1,255 real changes made)

. gen SumWrongVotes=NWrongChoice+2 if Against==1
(2,345 missing values generated)

. replace SumWrongVotes=NWrongChoice+1 if Neutral==1
(1,180 real changes made)

. replace SumWrongVotes=NWrongChoice if Supportive==1
(1,165 real changes made)

. 
. gen ProbRight=1 if SumRightVotes>SumWrongVotes
(1,395 missing values generated)

. replace ProbRight=0 if SumRightVotes<SumWrongVotes
(760 real changes made)

. replace ProbRight=0.5 if SumRightVotes==SumWrongVotes
(635 real changes made)

. 
. sort ElectionID

. by ElectionID: gen Quality=ProbRight if _n==1
(2,880 missing values generated)

. 
. 
. sort ElectorateID

. by ElectorateID: egen AverageQuality=mean(Quality)

. by ElectorateID: gen AQuality=AverageQuality if _n==1
(3,576 missing values generated)

. 
. 
. mean AQuality if Treatment=="ControlGroup"

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ------
             |       Mean   Std. Err.     [95% Conf. Int
> erval]
-------------+------------------------------------------
> ------
    AQuality |   .7611111   .0319362        .69082    .8
> 314022
--------------------------------------------------------
> ------

. mean AQuality if Treatment=="TreatmentGroup"

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ------
             |       Mean   Std. Err.     [95% Conf. Int
> erval]
-------------+------------------------------------------
> ------
    AQuality |   .6402778   .0362057      .5605896    .7
> 199659
--------------------------------------------------------
> ------

. 
. *Perform Mann-Whitney signrank tests, and Fisher-Pitma
> n permutation tests
. *to examine whether the experimental results of qualit
> y of democratic choice 
. *are different from the Max. Engagement Benchmark
. signrank AQuality=0.97 if Treatment=="ControlGroup"

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          39
    negative |       12          78          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties       -0.38
adjustment for zeros       0.00
                     ----------
adjusted variance        162.13

Ho: AQuality = 0.97 
             z =  -3.063
    Prob > |z| =   0.0022

. permtest1 AQuality=0.97 if Treatment=="ControlGroup"
Fisher-Pitman permutation test for paired replicates


 difference vector | AQuality-0.97 
-------------------+---------------------------------
 observations      | 12
  - positive       | 0
  - negative       | 12
  - zero           | 0
-------------------+---------------------------------
  critical value   | -2.506666674613952


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AQuality>=0.97  : p = .00024414
Test of hypothesis Ho: AQuality<=0.97  : p = 1
Test of hypothesis Ho: AQuality==0.97  : p = .00048828

. 
. signrank AQuality=0.97 if Treatment=="TreatmentGroup"

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          39
    negative |       12          78          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties       -0.13
adjustment for zeros       0.00
                     ----------
adjusted variance        162.38

Ho: AQuality = 0.97 
             z =  -3.061
    Prob > |z| =   0.0022

. permtest1 AQuality=0.97 if Treatment=="TreatmentGroup"
Fisher-Pitman permutation test for paired replicates


 difference vector | AQuality-0.97 
-------------------+---------------------------------
 observations      | 12
  - positive       | 0
  - negative       | 12
  - zero           | 0
-------------------+---------------------------------
  critical value   | -3.956666692495346


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AQuality>=0.97  : p = .00024414
Test of hypothesis Ho: AQuality<=0.97  : p = 1
Test of hypothesis Ho: AQuality==0.97  : p = .00048828

. restore

. 
. //////////////////////////////////////////////////////
> ////////////////////
> ////////////////                Figure 6              
>    /////////////////
> //////////////////////////////////////////////////////
> ////////////////////
> preserve

. //Based on the information elicted above, we make Figu
> re 6 using the following codes//
. clear

. import excel "D:\FiguresReplications.xlsx",  sheet("Fi
> gure6") firstrow

. twoway (bar Mean Position if Treatment=="ControlGroup"
> ,  name(Figure6,replace) fcolor(gs14) bcolor(gs4) lwid
> th(0.4) xaxis(1 2) yaxis(1 2) )||(bar Mean Position if
>  Treatment=="TreatmentGroup",  fcolor(gs6) bcolor(gs4)
>  lwidth(0.4)  )||(bar Mean Position if Treatment=="Ide
> al",  fcolor(white) bcolor(gs4) lwidth(0.4)  ),  ylabe
> l(0.5 (0.1) 1,nogrid) ylabel("",axis(2)) xlabel("",axi
> s(1)) xlabel("",axis(2)) ytitle("Quality of Democratic
>  Choice",size(large) height(5)) ytitle("",axis(2)) xti
> tle("") xtitle("",axis(2))       graphregion(color(whi
> te)) plotregion(color(white)) legend(off) text(0.84 0.
> 5 "Max",place(c) size(3) color(black)) text(0.82 0.5 "
> Engagement",place(c) size(3) color(black)) text(0.8 0.
> 5 "Benchmark",place(c) size(3) color(black)) text(0.70
>  1.5 "Control",place(c) size(3) color(black)) text(0.6
> 8 1.5 "Group",place(c) size(3) color(black)) text(0.62
>  2.5 "Treatment",place(c) size(3) color(black)) text(0
> .60 2.5 "Group",place(c) size(3) color(black)) text(0.
> 54 0.5 "0.97",place(c) size(huge) color(black)) text(0
> .54 1.5 "0.76",place(c) size(huge) color(black)) text(
> 0.54 2.5 "0.64",place(c) size(huge) color(black)) note
> ("Note: In both the control and treatment groups, the 
> estimates are based on" "actual votes of expert voters
>  whose willingness to vote {&ge} voting cost. We" "use
>  electorate as the unit of independent observation. We
>  use electorate" "level averages in the analysis and p
> erform Mann-Whitney and exact" "Fisher-Pitman permutat
> ion tests. The achieved quality of democratic" "choice
>  in each group is smaller than the max. eng. benchmark
>  (p<0.003)." ,span)

. graph display Figure6, xsize(6) ysize(6)

. graph export "D:\Figure6.pdf", as(pdf) replace
(file D:\Figure6.pdf written in PDF format)

. restore

. 
. 
. //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> ///////// Main Data Analysis of Section "Utilitarian P
> lanner" ////////
> //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> 
. *We compare experimental data of willingness to vote a
> nd the quality of democratic choice
. *to the Utilitarian Planner's prescriptions illustrate
> d in Figure 7
. *In this Empirical Replication file, we focus on the s
> tatistical analysis
. *The calculations of the utilitarian planner's prescri
> ptions are detailed in Online Appendix I 
. 
. preserve

. *We first focus on the behavior of expert voters in th
> e Treatment Group
. drop if Expertise==0
(1,089 observations deleted)

. drop if Treatment=="ControlGroup"
(1,251 observations deleted)

. 
. 
. /////////When Partisan Bias was Against and There was 
> 1 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVAgainst1=mean(Willi
> ngness2Vote) if Against==1&HowManyHaveExpertise==1
(1256 missing values generated)

. by ElectorateID, sort: egen AvergesAgainst1=mean(MeanW
> TVAgainst1)
(933 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffAgainst1=Averg
> esAgainst1 if _n==1
(1,257 missing values generated)

. gen QualityTreatmentAgaN1=0

. mean AVotingCutOffAgainst1

Mean estimation                   Number of obs   =     
>      3

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst1 |   5.833333   4.639804     -14.13
> 013                                                   
>         25.7968
--------------------------------------------------------
> ---------------

. mean QualityTreatmentAgaN1

Mean estimation                   Number of obs   =     
>  1,260

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentAgaN1 |          0  (omitted)
--------------------------------------------------------
> ---------------

. signrank  AVotingCutOffAgainst1=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        2           5         2.5
    negative |        0           0         2.5
        zero |        1           1           1
-------------+---------------------------------
         all |        3           6           6

unadjusted variance        3.50
adjustment for ties        0.00
adjustment for zeros      -0.25
                     ----------
adjusted variance          3.25

Ho: AVotingCutOffAgainst1 = 0
             z =   1.387
    Prob > |z| =   0.1655

. permtest1  AVotingCutOffAgainst1=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffAgainst1-0
-------------------+---------------------------------
 observations      | 3
  - positive       | 2
  - negative       | 0
  - zero           | 1
-------------------+---------------------------------
  critical value   | 17.5


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffAgainst1>=0 : p = 1
Test of hypothesis Ho: AVotingCutOffAgainst1<=0 : p = .2
> 5
Test of hypothesis Ho: AVotingCutOffAgainst1==0 : p = .5

. 
. /////////When Partisan Bias was Against and There were
>  2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVAgainst2=mean(Willi
> ngness2Vote) if Against==1&HowManyHaveExpertise==2
(1234 missing values generated)

. by ElectorateID, sort: egen AvergesAgainst2=mean(MeanW
> TVAgainst2)
(432 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffAgainst2=Averg
> esAgainst2 if _n==1
(1,252 missing values generated)

. gen QualityTreatmentAgaN2=(AVotingCutOffAgainst2/100)^
> 2
(1,252 missing values generated)

. mean AVotingCutOffAgainst2

Mean estimation                   Number of obs   =     
>      8

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst2 |   27.26042   6.667995      11.49
> 311                                                   
>        43.02772
--------------------------------------------------------
> ---------------

. mean QualityTreatmentAgaN2

Mean estimation                   Number of obs   =     
>      8

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentAgaN2 |   .1054365   .0337554      .0256
> 176                                                   
>        .1852555
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentAgaN2=1

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          18
    negative |        8          36          18
        zero |        0           0           0
-------------+---------------------------------
         all |        8          36          36

unadjusted variance       51.00
adjustment for ties       -0.13
adjustment for zeros       0.00
                     ----------
adjusted variance         50.88

Ho: QualityTreatmentAgaN2 = 1
             z =  -2.524
    Prob > |z| =   0.0116

. permtest1 QualityTreatmentAgaN2=1
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentAgaN2-1
-------------------+---------------------------------
 observations      | 8
  - positive       | 0
  - negative       | 8
  - zero           | 0
-------------------+---------------------------------
  critical value   | -7.156507655819951


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentAgaN2>=1 : p = .0
> 0390625
Test of hypothesis Ho: QualityTreatmentAgaN2<=1 : p = 1
Test of hypothesis Ho: QualityTreatmentAgaN2==1 : p = .0
> 078125

. signrank  AVotingCutOffAgainst2=100

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          18
    negative |        8          36          18
        zero |        0           0           0
-------------+---------------------------------
         all |        8          36          36

unadjusted variance       51.00
adjustment for ties       -0.13
adjustment for zeros       0.00
                     ----------
adjusted variance         50.88

Ho: AVotingCutOffAgainst2 = 100
             z =  -2.524
    Prob > |z| =   0.0116

. permtest1  AVotingCutOffAgainst2=100
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffAgainst2-100
-------------------+---------------------------------
 observations      | 8
  - positive       | 0
  - negative       | 8
  - zero           | 0
-------------------+---------------------------------
  critical value   | -581.9166679382324


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffAgainst2>=100 : p = 
> .00390625
Test of hypothesis Ho: AVotingCutOffAgainst2<=100 : p = 
> 1
Test of hypothesis Ho: AVotingCutOffAgainst2==100 : p = 
> .0078125

. 
. /////////When Partisan Bias was Against and There were
>  3 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVAgainst3=mean(Willi
> ngness2Vote) if Against==1&HowManyHaveExpertise==3
(1140 missing values generated)

. by ElectorateID, sort: egen AvergesAgainst3=mean(MeanW
> TVAgainst3)
(112 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffAgainst3=Averg
> esAgainst3 if _n==1
(1,249 missing values generated)

. gen QualityTreatmentAgaN3=comb(3,3)*(AVotingCutOffAgai
> nst3/100)^3+0.5*comb(3,2)*((AVotingCutOffAgainst3/100)
> ^2)*(1-(AVotingCutOffAgainst3/100))
(1,249 missing values generated)

. mean AVotingCutOffAgainst3

Mean estimation                   Number of obs   =     
>     11

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst3 |   35.41306   3.641884      27.29
> 844                                                   
>        43.52768
--------------------------------------------------------
> ---------------

. mean QualityTreatmentAgaN3

Mean estimation                   Number of obs   =     
>     11

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentAgaN3 |   .1779707   .0354245        .09
> 904                                                   
>        .2569014
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentAgaN3=1

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          33
    negative |       11          66          33
        zero |        0           0           0
-------------+---------------------------------
         all |       11          66          66

unadjusted variance      126.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        126.50

Ho: QualityTreatmentAgaN3 = 1
             z =  -2.934
    Prob > |z| =   0.0033

. permtest1 QualityTreatmentAgaN3=1
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentAgaN3-1
-------------------+---------------------------------
 observations      | 11
  - positive       | 0
  - negative       | 11
  - zero           | 0
-------------------+---------------------------------
  critical value   | -9.042322549968958


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentAgaN3>=1 : p = .0
> 0048828
Test of hypothesis Ho: QualityTreatmentAgaN3<=1 : p = 1
Test of hypothesis Ho: QualityTreatmentAgaN3==1 : p = .0
> 0097656

. signrank  AVotingCutOffAgainst3=100

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          33
    negative |       11          66          33
        zero |        0           0           0
-------------+---------------------------------
         all |       11          66          66

unadjusted variance      126.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        126.50

Ho: AVotingCutOffAgainst3 = 100
             z =  -2.934
    Prob > |z| =   0.0033

. permtest1  AVotingCutOffAgainst3=100
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffAgainst3-100
-------------------+---------------------------------
 observations      | 11
  - positive       | 0
  - negative       | 11
  - zero           | 0
-------------------+---------------------------------
  critical value   | -710.4563522338867


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffAgainst3>=100 : p = 
> .00048828
Test of hypothesis Ho: AVotingCutOffAgainst3<=100 : p = 
> 1
Test of hypothesis Ho: AVotingCutOffAgainst3==100 : p = 
> .00097656

. 
. /////////When Partisan Bias was Against and There were
>  4 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVAgainst4=mean(Willi
> ngness2Vote) if Against==1&HowManyHaveExpertise==4
(1048 missing values generated)

. by ElectorateID, sort: egen AvergesAgainst4=mean(MeanW
> TVAgainst4)

. by ElectorateID, sort: gen AVotingCutOffAgainst4=Averg
> esAgainst4 if _n==1
(1,248 missing values generated)

. gen QualityTreatmentAgaN4=comb(4,3)*((AVotingCutOffAga
> inst4/100)^3)*(1-(AVotingCutOffAgainst4/100))+0.5*comb
> (4,2)*((AVotingCutOffAgainst4/100)^2)*(1-(AVotingCutOf
> fAgainst3/100)^2)
(1,249 missing values generated)

. mean AVotingCutOffAgainst4

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst4 |   34.32882   3.422976       26.7
> 949                                                   
>        41.86274
--------------------------------------------------------
> ---------------

. mean QualityTreatmentAgaN4

Mean estimation                   Number of obs   =     
>     11

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentAgaN4 |   .4638175   .1015254      .2376
> 048                                                   
>        .6900302
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentAgaN4=0.951638

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           2          33
    negative |       10          64          33
        zero |        0           0           0
-------------+---------------------------------
         all |       11          66          66

unadjusted variance      126.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        126.50

Ho: QualityTreatmentAgaN4 = 0.951638
             z =  -2.756
    Prob > |z| =   0.0058

. permtest1 QualityTreatmentAgaN4=0.951638
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentAgaN4-0.951638
-------------------+---------------------------------
 observations      | 11
  - positive       | 1
  - negative       | 10
  - zero           | 0
-------------------+---------------------------------
  critical value   | -5.366025221519946


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentAgaN4>=0.951638 :
>  p = .00146484
Test of hypothesis Ho: QualityTreatmentAgaN4<=0.951638 :
>  p = .99902344
Test of hypothesis Ho: QualityTreatmentAgaN4==0.951638 :
>  p = .00292969

. signrank  AVotingCutOffAgainst4=86.7

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          39
    negative |       12          78          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffAgainst4 = 86.7
             z =  -3.059
    Prob > |z| =   0.0022

. permtest1  AVotingCutOffAgainst4=86.7
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffAgainst4-86.7
-------------------+---------------------------------
 observations      | 12
  - positive       | 0
  - negative       | 12
  - zero           | 0
-------------------+---------------------------------
  critical value   | -628.4541667938233


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffAgainst4>=86.7 : p =
>  .00024414
Test of hypothesis Ho: AVotingCutOffAgainst4<=86.7 : p =
>  1
Test of hypothesis Ho: AVotingCutOffAgainst4==86.7 : p =
>  .00048828

. 
. /////////When Partisan Bias was Against and There were
>  5 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVAgainst5=mean(Willi
> ngness2Vote) if Against==1&HowManyHaveExpertise==5
(1200 missing values generated)

. by ElectorateID, sort: egen AvergesAgainst5=mean(MeanW
> TVAgainst5)
(416 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffAgainst5=Averg
> esAgainst5 if _n==1
(1,252 missing values generated)

. gen QualityTreatmentAgaN5=comb(5,3)*((AVotingCutOffAga
> inst5/100)^3)*(1-(AVotingCutOffAgainst4/100))^2+0.5*co
> mb(5,2)*((AVotingCutOffAgainst5/100)^2)*(1-(AVotingCut
> OffAgainst3/100)^5)
(1,253 missing values generated)

. mean AVotingCutOffAgainst5

Mean estimation                   Number of obs   =     
>      8

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst5 |    29.6875   4.147264      19.88
> 078                                                   
>        39.49422
--------------------------------------------------------
> ---------------

. mean QualityTreatmentAgaN5

Mean estimation                   Number of obs   =     
>      7

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentAgaN5 |   .6443061   .1963658      .1638
> 163                                                   
>        1.124796
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentAgaN5=0.880517

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        2           8          14
    negative |        5          20          14
        zero |        0           0           0
-------------+---------------------------------
         all |        7          28          28

unadjusted variance       35.00
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         35.00

Ho: QualityTreatmentAgaN5 = 0.880517
             z =  -1.014
    Prob > |z| =   0.3105

. permtest1 QualityTreatmentAgaN5=0.880517
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentAgaN5-0.880517
-------------------+---------------------------------
 observations      | 7
  - positive       | 2
  - negative       | 5
  - zero           | 0
-------------------+---------------------------------
  critical value   | -1.653476122302055


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentAgaN5>=0.880517 :
>  p = .15625
Test of hypothesis Ho: QualityTreatmentAgaN5<=0.880517 :
>  p = .8515625
Test of hypothesis Ho: QualityTreatmentAgaN5==0.880517 :
>  p = .3125

. signrank  AVotingCutOffAgainst5=67.5

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          18
    negative |        8          36          18
        zero |        0           0           0
-------------+---------------------------------
         all |        8          36          36

unadjusted variance       51.00
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         51.00

Ho: AVotingCutOffAgainst5 = 67.5
             z =  -2.521
    Prob > |z| =   0.0117

. permtest1  AVotingCutOffAgainst5=67.5
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffAgainst5-67.5
-------------------+---------------------------------
 observations      | 8
  - positive       | 0
  - negative       | 8
  - zero           | 0
-------------------+---------------------------------
  critical value   | -302.5


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffAgainst5>=67.5 : p =
>  .00390625
Test of hypothesis Ho: AVotingCutOffAgainst5<=67.5 : p =
>  1
Test of hypothesis Ho: AVotingCutOffAgainst5==67.5 : p =
>  .0078125

. 
. 
. /////////When Partisan Bias was Neutral and There was 
> 1 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVNeutral1=mean(Willi
> ngness2Vote) if Neutral==1&HowManyHaveExpertise==1
(1257 missing values generated)

. by ElectorateID, sort: egen AvergesNeutral1=mean(MeanW
> TVNeutral1)
(961 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffNeutral1=Averg
> esNeutral1 if _n==1
(1,257 missing values generated)

. gen QualityTreatmentNeuN1=1-0.5*(1-AVotingCutOffNeutra
> l1/100)
(1,257 missing values generated)

. mean AVotingCutOffNeutral1

Mean estimation                   Number of obs   =     
>      3

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral1 |   23.33333   14.52966     -39.18
> 276                                                   
>        85.84943
--------------------------------------------------------
> ---------------

. mean QualityTreatmentNeuN1

Mean estimation                   Number of obs   =     
>      3

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentNeuN1 |   .6166667   .0726483      .3040
> 862                                                   
>        .9292471
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentNeuN1=1

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0           3
    negative |        3           6           3
        zero |        0           0           0
-------------+---------------------------------
         all |        3           6           6

unadjusted variance        3.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance          3.50

Ho: QualityTreatmentNeuN1 = 1
             z =  -1.604
    Prob > |z| =   0.1088

. permtest1 QualityTreatmentNeuN1=1
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentNeuN1-1
-------------------+---------------------------------
 observations      | 3
  - positive       | 0
  - negative       | 3
  - zero           | 0
-------------------+---------------------------------
  critical value   | -1.149999976158142


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentNeuN1>=1 : p = .1
> 25
Test of hypothesis Ho: QualityTreatmentNeuN1<=1 : p = 1
Test of hypothesis Ho: QualityTreatmentNeuN1==1 : p = .2
> 5

. signrank  AVotingCutOffNeutral1=100

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0           3
    negative |        3           6           3
        zero |        0           0           0
-------------+---------------------------------
         all |        3           6           6

unadjusted variance        3.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance          3.50

Ho: AVotingCutOffNeutral1 = 100
             z =  -1.604
    Prob > |z| =   0.1088

. permtest1  AVotingCutOffNeutral1=100
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffNeutral1-100
-------------------+---------------------------------
 observations      | 3
  - positive       | 0
  - negative       | 3
  - zero           | 0
-------------------+---------------------------------
  critical value   | -230


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffNeutral1>=100 : p = 
> .125
Test of hypothesis Ho: AVotingCutOffNeutral1<=100 : p = 
> 1
Test of hypothesis Ho: AVotingCutOffNeutral1==100 : p = 
> .25

. 
. /////////When Partisan Bias was Neutral and There were
>  2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVNeutral2=mean(Willi
> ngness2Vote) if Neutral==1&HowManyHaveExpertise==2
(1232 missing values generated)

. by ElectorateID, sort: egen AvergesNeutral2=mean(MeanW
> TVNeutral2)
(325 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffNeutral2=Averg
> esNeutral2 if _n==1
(1,251 missing values generated)

. gen QualityTreatmentNeuN2=1-0.5*(1-AVotingCutOffNeutra
> l2/100)^2
(1,251 missing values generated)

. mean AVotingCutOffNeutral2

Mean estimation                   Number of obs   =     
>      9

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral2 |   31.16667   5.608928      18.23
> 246                                                   
>        44.10088
--------------------------------------------------------
> ---------------

. mean QualityTreatmentNeuN2

Mean estimation                   Number of obs   =     
>      9

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentNeuN2 |   .7505146   .0354732      .6687
> 133                                                   
>        .8323159
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentNeuN2=0.959184

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0        22.5
    negative |        9          45        22.5
        zero |        0           0           0
-------------+---------------------------------
         all |        9          45          45

unadjusted variance       71.25
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         71.25

Ho: QualityTreatmentNeuN2 = 0.959184
             z =  -2.666
    Prob > |z| =   0.0077

. permtest1 QualityTreatmentNeuN2=0.959184
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentNeuN2-0.959184
-------------------+---------------------------------
 observations      | 9
  - positive       | 0
  - negative       | 9
  - zero           | 0
-------------------+---------------------------------
  critical value   | -1.878024778705598


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentNeuN2>=0.959184 :
>  p = .00195313
Test of hypothesis Ho: QualityTreatmentNeuN2<=0.959184 :
>  p = 1
Test of hypothesis Ho: QualityTreatmentNeuN2==0.959184 :
>  p = .00390625

. signrank  AVotingCutOffNeutral2=71.4

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0        22.5
    negative |        9          45        22.5
        zero |        0           0           0
-------------+---------------------------------
         all |        9          45          45

unadjusted variance       71.25
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         71.25

Ho: AVotingCutOffNeutral2 = 71.4
             z =  -2.666
    Prob > |z| =   0.0077

. permtest1  AVotingCutOffNeutral2=71.4
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffNeutral2-71.4
-------------------+---------------------------------
 observations      | 9
  - positive       | 0
  - negative       | 9
  - zero           | 0
-------------------+---------------------------------
  critical value   | -362.1


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffNeutral2>=71.4 : p =
>  .00195313
Test of hypothesis Ho: AVotingCutOffNeutral2<=71.4 : p =
>  1
Test of hypothesis Ho: AVotingCutOffNeutral2==71.4 : p =
>  .00390625

. 
. /////////When Partisan Bias was Neutral and There were
>  3 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVNeutral3=mean(Willi
> ngness2Vote) if Neutral==1&HowManyHaveExpertise==3
(1146 missing values generated)

. by ElectorateID, sort: egen AvergesNeutral3=mean(MeanW
> TVNeutral3)

. by ElectorateID, sort: gen AVotingCutOffNeutral3=Averg
> esNeutral3 if _n==1
(1,248 missing values generated)

. gen QualityTreatmentNeuN3=1-0.5*(1-AVotingCutOffNeutra
> l3/100)^3
(1,248 missing values generated)

. mean AVotingCutOffNeutral3

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral3 |   29.35231   2.229159      24.44
> 597                                                   
>        34.25866
--------------------------------------------------------
> ---------------

. mean QualityTreatmentNeuN3

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentNeuN3 |   .8179367   .0167815      .7810
> 009                                                   
>        .8548725
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentNeuN3=0.950269

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          39
    negative |       12          78          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties       -0.13
adjustment for zeros       0.00
                     ----------
adjusted variance        162.38

Ho: QualityTreatmentNeuN3 = 0.950269
             z =  -3.061
    Prob > |z| =   0.0022

. permtest1 QualityTreatmentNeuN3=0.950269
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentNeuN3-0.950269
-------------------+---------------------------------
 observations      | 12
  - positive       | 0
  - negative       | 12
  - zero           | 0
-------------------+---------------------------------
  critical value   | -1.587987676456452


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentNeuN3>=0.950269 :
>  p = .00024414
Test of hypothesis Ho: QualityTreatmentNeuN3<=0.950269 :
>  p = 1
Test of hypothesis Ho: QualityTreatmentNeuN3==0.950269 :
>  p = .00048828

. signrank  AVotingCutOffNeutral3=53.7

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          39
    negative |       12          78          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties       -0.13
adjustment for zeros       0.00
                     ----------
adjusted variance        162.38

Ho: AVotingCutOffNeutral3 = 53.7
             z =  -3.061
    Prob > |z| =   0.0022

. permtest1  AVotingCutOffNeutral3=53.7
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffNeutral3-53.7
-------------------+---------------------------------
 observations      | 12
  - positive       | 0
  - negative       | 12
  - zero           | 0
-------------------+---------------------------------
  critical value   | -292.1722206115723


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffNeutral3>=53.7 : p =
>  .00024414
Test of hypothesis Ho: AVotingCutOffNeutral3<=53.7 : p =
>  1
Test of hypothesis Ho: AVotingCutOffNeutral3==53.7 : p =
>  .00048828

. 
. /////////When Partisan Bias was Neutral and There were
>  4 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVNeutral4=mean(Willi
> ngness2Vote) if Neutral==1&HowManyHaveExpertise==4
(1084 missing values generated)

. by ElectorateID, sort: egen AvergesNeutral4=mean(MeanW
> TVNeutral4)

. by ElectorateID, sort: gen AVotingCutOffNeutral4=Averg
> esNeutral4 if _n==1
(1,248 missing values generated)

. gen QualityTreatmentNeuN4=1-0.5*(1-AVotingCutOffNeutra
> l4/100)^4
(1,248 missing values generated)

. mean AVotingCutOffNeutral4

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral4 |   28.91771   2.884807      22.56
> 829                                                   
>        35.26713
--------------------------------------------------------
> ---------------

. mean QualityTreatmentNeuN4

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentNeuN4 |   .8585247   .0214247      .8113
> 691                                                   
>        .9056802
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentNeuN4=0.950828

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           1          39
    negative |       11          77          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: QualityTreatmentNeuN4 = 0.950828
             z =  -2.981
    Prob > |z| =   0.0029

. permtest1 QualityTreatmentNeuN4=0.950828
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentNeuN4-0.950828
-------------------+---------------------------------
 observations      | 12
  - positive       | 1
  - negative       | 11
  - zero           | 0
-------------------+---------------------------------
  critical value   | -1.107639838348388


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentNeuN4>=0.950828 :
>  p = .00048828
Test of hypothesis Ho: QualityTreatmentNeuN4<=0.950828 :
>  p = .99975586
Test of hypothesis Ho: QualityTreatmentNeuN4==0.950828 :
>  p = .00097656

. signrank  AVotingCutOffNeutral4=44

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           1          39
    negative |       11          77          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffNeutral4 = 44
             z =  -2.981
    Prob > |z| =   0.0029

. permtest1  AVotingCutOffNeutral4=44
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffNeutral4-44
-------------------+---------------------------------
 observations      | 12
  - positive       | 1
  - negative       | 11
  - zero           | 0
-------------------+---------------------------------
  critical value   | -180.9875001907349


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffNeutral4>=44 : p = .
> 00048828
Test of hypothesis Ho: AVotingCutOffNeutral4<=44 : p = .
> 99975586
Test of hypothesis Ho: AVotingCutOffNeutral4==44 : p = .
> 00097656

. 
. /////////When Partisan Bias was Neutral and There were
>  5 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVNeutral5=mean(Willi
> ngness2Vote) if Neutral==1&HowManyHaveExpertise==5
(1155 missing values generated)

. by ElectorateID, sort: egen AvergesNeutral5=mean(MeanW
> TVNeutral5)
(207 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffNeutral5=Averg
> esNeutral5 if _n==1
(1,250 missing values generated)

. gen QualityTreatmentNeuN5=1-0.5*(1-AVotingCutOffNeutra
> l5/100)^5
(1,250 missing values generated)

. mean AVotingCutOffNeutral5

Mean estimation                   Number of obs   =     
>     10

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral5 |      28.63   3.575815      20.54
> 094                                                   
>        36.71906
--------------------------------------------------------
> ---------------

. mean QualityTreatmentNeuN5

Mean estimation                   Number of obs   =     
>     10

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentNeuN5 |    .887612   .0234631      .8345
> 348                                                   
>        .9406893
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentNeuN5=0.953074

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           4        27.5
    negative |        9          51        27.5
        zero |        0           0           0
-------------+---------------------------------
         all |       10          55          55

unadjusted variance       96.25
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         96.25

Ho: QualityTreatmentNeuN5 = 0.953074
             z =  -2.395
    Prob > |z| =   0.0166

. permtest1 QualityTreatmentNeuN5=0.953074
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentNeuN5-0.953074
-------------------+---------------------------------
 observations      | 10
  - positive       | 1
  - negative       | 9
  - zero           | 0
-------------------+---------------------------------
  critical value   | -.6546197307014461


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentNeuN5>=0.953074 :
>  p = .00878906
Test of hypothesis Ho: QualityTreatmentNeuN5<=0.953074 :
>  p = .9921875
Test of hypothesis Ho: QualityTreatmentNeuN5==0.953074 :
>  p = .01757813

. signrank  AVotingCutOffNeutral5=37.7

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           7        27.5
    negative |        9          48        27.5
        zero |        0           0           0
-------------+---------------------------------
         all |       10          55          55

unadjusted variance       96.25
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         96.25

Ho: AVotingCutOffNeutral5 = 37.7
             z =  -2.090
    Prob > |z| =   0.0367

. permtest1  AVotingCutOffNeutral5=37.7
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffNeutral5-37.7
-------------------+---------------------------------
 observations      | 10
  - positive       | 1
  - negative       | 9
  - zero           | 0
-------------------+---------------------------------
  critical value   | -90.69999885559085


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffNeutral5>=37.7 : p =
>  .01660156
Test of hypothesis Ho: AVotingCutOffNeutral5<=37.7 : p =
>  .984375
Test of hypothesis Ho: AVotingCutOffNeutral5==37.7 : p =
>  .03320313

. 
. 
. /////////When Partisan Bias was Supportive and There w
> as 1 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVSupportive1=mean(Wi
> llingness2Vote) if Supportive==1&HowManyHaveExpertise=
> =1
(1258 missing values generated)

. by ElectorateID, sort: egen AvergesSupportive1=mean(Me
> anWTVSupportive1)
(1158 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffSupportive1=Av
> ergesSupportive1 if _n==1
(1,259 missing values generated)

. gen QualityTreatmentSuppN1=1

. mean AVotingCutOffSupportive1

Mean estimation                   Number of obs   =     
>      1

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive1 |       37.5          .        
>      .                                                
>                  .
--------------------------------------------------------
> ------------------

. signrank AVotingCutOffSupportive1=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           1          .5
    negative |        0           0          .5
        zero |        0           0           0
-------------+---------------------------------
         all |        1           1           1

unadjusted variance        0.25
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance          0.25

Ho: AVotingCutOffSupportive1 = 0
             z =   1.000
    Prob > |z| =   0.3173

. permtest1 AVotingCutOffSupportive1=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffSupportive1-0
-------------------+---------------------------------
 observations      | 1
  - positive       | 1
  - negative       | 0
  - zero           | 0
-------------------+---------------------------------
  critical value   | 37.5


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffSupportive1>=0 : p =
>  1
Test of hypothesis Ho: AVotingCutOffSupportive1<=0 : p =
>  .5
Test of hypothesis Ho: AVotingCutOffSupportive1==0 : p =
>  1

. 
. 
. /////////When Partisan Bias was Supportive and There w
> ere 2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVSupportive2=mean(Wi
> llingness2Vote) if Supportive==1&HowManyHaveExpertise=
> =2
(1230 missing values generated)

. by ElectorateID, sort: egen AvergesSupportive2=mean(Me
> anWTVSupportive2)
(209 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffSupportive2=Av
> ergesSupportive2 if _n==1
(1,250 missing values generated)

. gen QualityTreatmentSuppN2=1

. mean AVotingCutOffSupportive2

Mean estimation                   Number of obs   =     
>     10

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive2 |       8.35   2.636601      2.
> 385593                                                
>           14.31441
--------------------------------------------------------
> ------------------

. signrank AVotingCutOffSupportive2=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        9          54          27
    negative |        0           0          27
        zero |        1           1           1
-------------+---------------------------------
         all |       10          55          55

unadjusted variance       96.25
adjustment for ties       -0.13
adjustment for zeros      -0.25
                     ----------
adjusted variance         95.88

Ho: AVotingCutOffSupportive2 = 0
             z =   2.757
    Prob > |z| =   0.0058

. permtest1 AVotingCutOffSupportive2=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffSupportive2-0
-------------------+---------------------------------
 observations      | 10
  - positive       | 9
  - negative       | 0
  - zero           | 1
-------------------+---------------------------------
  critical value   | 83.5


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffSupportive2>=0 : p =
>  1
Test of hypothesis Ho: AVotingCutOffSupportive2<=0 : p =
>  .00195313
Test of hypothesis Ho: AVotingCutOffSupportive2==0 : p =
>  .00390625

. 
. /////////When Partisan Bias was Supportive and There w
> ere 2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVSupportive3=mean(Wi
> llingness2Vote) if Supportive==1&HowManyHaveExpertise=
> =3
(1125 missing values generated)

. by ElectorateID, sort: egen AvergesSupportive3=mean(Me
> anWTVSupportive3)

. by ElectorateID, sort: gen AVotingCutOffSupportive3=Av
> ergesSupportive3 if _n==1
(1,248 missing values generated)

. gen QualityTreatmentSuppN3=1

. mean AVotingCutOffSupportive3

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive3 |   16.18843   2.983253       9
> .62233                                                
>           22.75452
--------------------------------------------------------
> ------------------

. signrank AVotingCutOffSupportive3=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |       12          78          39
    negative |        0           0          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffSupportive3 = 0
             z =   3.059
    Prob > |z| =   0.0022

. permtest1 AVotingCutOffSupportive3=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffSupportive3-0
-------------------+---------------------------------
 observations      | 12
  - positive       | 12
  - negative       | 0
  - zero           | 0
-------------------+---------------------------------
  critical value   | 194.2611126899719


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffSupportive3>=0 : p =
>  1
Test of hypothesis Ho: AVotingCutOffSupportive3<=0 : p =
>  .00024414
Test of hypothesis Ho: AVotingCutOffSupportive3==0 : p =
>  .00048828

. 
. /////////When Partisan Bias was Supportive and There w
> ere 2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVSupportive4=mean(Wi
> llingness2Vote) if Supportive==1&HowManyHaveExpertise=
> =4
(1120 missing values generated)

. by ElectorateID, sort: egen AvergesSupportive4=mean(Me
> anWTVSupportive4)

. by ElectorateID, sort: gen AVotingCutOffSupportive4=Av
> ergesSupportive4 if _n==1
(1,248 missing values generated)

. gen QualityTreatmentSuppN4=1

. mean AVotingCutOffSupportive4

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive4 |   11.72535   1.928021      7.
> 481802                                                
>           15.96889
--------------------------------------------------------
> ------------------

. signrank AVotingCutOffSupportive4=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |       12          78          39
    negative |        0           0          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffSupportive4 = 0
             z =   3.059
    Prob > |z| =   0.0022

. permtest1 AVotingCutOffSupportive4=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffSupportive4-0
-------------------+---------------------------------
 observations      | 12
  - positive       | 12
  - negative       | 0
  - zero           | 0
-------------------+---------------------------------
  critical value   | 140.7041683197021


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffSupportive4>=0 : p =
>  1
Test of hypothesis Ho: AVotingCutOffSupportive4<=0 : p =
>  .00024414
Test of hypothesis Ho: AVotingCutOffSupportive4==0 : p =
>  .00048828

. 
. /////////When Partisan Bias was Supportive and There w
> ere 2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVSupportive5=mean(Wi
> llingness2Vote) if Supportive==1&HowManyHaveExpertise=
> =5
(1155 missing values generated)

. by ElectorateID, sort: egen AvergesSupportive5=mean(Me
> anWTVSupportive5)
(103 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffSupportive5=Av
> ergesSupportive5 if _n==1
(1,249 missing values generated)

. gen QualityTreatmentSuppN5=1

. mean AVotingCutOffSupportive5

Mean estimation                   Number of obs   =     
>     11

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive5 |   13.09091   3.413748      5.
> 484604                                                
>           20.69721
--------------------------------------------------------
> ------------------

. signrank AVotingCutOffSupportive5=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |       11          66          33
    negative |        0           0          33
        zero |        0           0           0
-------------+---------------------------------
         all |       11          66          66

unadjusted variance      126.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        126.50

Ho: AVotingCutOffSupportive5 = 0
             z =   2.934
    Prob > |z| =   0.0033

. permtest1 AVotingCutOffSupportive5=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffSupportive5-0
-------------------+---------------------------------
 observations      | 11
  - positive       | 11
  - negative       | 0
  - zero           | 0
-------------------+---------------------------------
  critical value   | 143.9999990463257


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffSupportive5>=0 : p =
>  1
Test of hypothesis Ho: AVotingCutOffSupportive5<=0 : p =
>  .00048828
Test of hypothesis Ho: AVotingCutOffSupportive5==0 : p =
>  .00097656

. 
. restore

. 
. 
. 
. preserve

. *Now we focus on the behavior of expert voters in the 
> Control Group
. drop if Expertise==0
(1,089 observations deleted)

. drop if Treatment=="TreatmentGroup"
(1,260 observations deleted)

. 
. //////////      When the partisan bias is Against     
>  //////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVAgainst=mean(Willin
> gness2Vote) if Against==1
(788 missing values generated)

. by ElectorateID, sort: egen AvergesAgainst=mean(MeanWT
> VAgainst)

. by ElectorateID, sort: gen AVotingCutOffAgainst=Averge
> sAgainst if _n==1
(1,239 missing values generated)

. gen QualityTreatmentAga=comb(5,3)*(0.7*(AVotingCutOffA
> gainst/100))^3*(1-(0.7*(AVotingCutOffAgainst/100)))^2+
> comb(5,4)*(0.7*(AVotingCutOffAgainst/100))^4*(1-(0.7*(
> AVotingCutOffAgainst/100)))^1+comb(5,5)*(0.7*(AVotingC
> utOffAgainst/100))^5+0.5*comb(5,2)*((0.7*(AVotingCutOf
> fAgainst/100))^2)*(1-(0.7*(AVotingCutOffAgainst/100)))
> ^3
(1,239 missing values generated)

. mean AVotingCutOffAgainst

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> --------------
                     |       Mean   Std. Err.     [95% C
> on                                                    
>   f. Interval]
---------------------+----------------------------------
> --------------
AVotingCutOffAgainst |   51.82489   2.911182      45.417
> 42                                                    
>       58.23236
--------------------------------------------------------
> --------------

. mean QualityTreatmentAga

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> -------------
                    |       Mean   Std. Err.     [95% Co
> n                                                     
>  f. Interval]
--------------------+-----------------------------------
> -------------
QualityTreatmentAga |    .425564   .0346559      .349286
> 9                                                     
>      .5018412
--------------------------------------------------------
> -------------

. signrank QualityTreatmentAga=0.878986

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          39
    negative |       12          78          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: QualityTreatmentAga = 0.878986
             z =  -3.059
    Prob > |z| =   0.0022

. permtest1 QualityTreatmentAga=0.878986
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentAga-0.878986
-------------------+---------------------------------
 observations      | 12
  - positive       | 0
  - negative       | 12
  - zero           | 0
-------------------+---------------------------------
  critical value   | -5.4410634068079


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentAga>=0.878986 : p
>  = .00024414
Test of hypothesis Ho: QualityTreatmentAga<=0.878986 : p
>  = 1
Test of hypothesis Ho: QualityTreatmentAga==0.878986 : p
>  = .00048828

. signrank  AVotingCutOffAgainst=96.2

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          39
    negative |       12          78          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffAgainst = 96.2
             z =  -3.059
    Prob > |z| =   0.0022

. permtest1  AVotingCutOffAgainst=96.2
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffAgainst-96.2
-------------------+---------------------------------
 observations      | 12
  - positive       | 0
  - negative       | 12
  - zero           | 0
-------------------+---------------------------------
  critical value   | -532.5013145446778


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffAgainst>=96.2 : p = 
> .00024414
Test of hypothesis Ho: AVotingCutOffAgainst<=96.2 : p = 
> 1
Test of hypothesis Ho: AVotingCutOffAgainst==96.2 : p = 
> .00048828

. 
. //////////      When the partisan bias is Neutral     
>  //////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVNeutral=mean(Willin
> gness2Vote) if Neutral==1
(859 missing values generated)

. by ElectorateID, sort: egen AvergesNeutral=mean(MeanWT
> VNeutral)

. by ElectorateID, sort: gen AVotingCutOffNeutral=Averge
> sNeutral if _n==1
(1,239 missing values generated)

. gen QualityTreatmentNeu=comb(5,1)*(0.7*(AVotingCutOffN
> eutral/100))*(1-(0.7*(AVotingCutOffNeutral/100)))^4+co
> mb(5,2)*(0.7*(AVotingCutOffNeutral/100))^2*(1-(0.7*(AV
> otingCutOffNeutral/100)))^3+comb(5,3)*(0.7*(AVotingCut
> OffNeutral/100))^3*(1-(0.7*(AVotingCutOffNeutral/100))
> )^2+comb(5,4)*(0.7*(AVotingCutOffNeutral/100))^4*(1-(0
> .7*(AVotingCutOffNeutral/100)))^1+comb(5,5)*(0.7*(AVot
> ingCutOffNeutral/100))^5+0.5*comb(5,0)*((0.7*(AVotingC
> utOffNeutral/100))^0)*(1-(0.7*(AVotingCutOffNeutral/10
> 0)))^5
(1,239 missing values generated)

. mean AVotingCutOffNeutral

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> --------------
                     |       Mean   Std. Err.     [95% C
> on                                                    
>   f. Interval]
---------------------+----------------------------------
> --------------
AVotingCutOffNeutral |   47.46382   3.245181      40.321
> 22                                                    
>       54.60641
--------------------------------------------------------
> --------------

. mean QualityTreatmentNeu

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> -------------
                    |       Mean   Std. Err.     [95% Co
> n                                                     
>  f. Interval]
--------------------+-----------------------------------
> -------------
QualityTreatmentNeu |   .9246114   .0137732      .894296
> 9                                                     
>       .954926
--------------------------------------------------------
> -------------

. signrank QualityTreatmentNeu=0.93614

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        6          34          39
    negative |        6          44          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: QualityTreatmentNeu = 0.93614
             z =  -0.392
    Prob > |z| =   0.6949

. permtest1 QualityTreatmentNeu=0.93614
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentNeu-0.93614
-------------------+---------------------------------
 observations      | 12
  - positive       | 6
  - negative       | 6
  - zero           | 0
-------------------+---------------------------------
  critical value   | -.1383426091003416


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentNeu>=0.93614 : p 
> = .24584961
Test of hypothesis Ho: QualityTreatmentNeu<=0.93614 : p 
> = .75439453
Test of hypothesis Ho: QualityTreatmentNeu==0.93614 : p 
> = .49169922

. signrank  AVotingCutOffNeutral=48.2

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        6          38          39
    negative |        6          40          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffNeutral = 48.2
             z =  -0.078
    Prob > |z| =   0.9375

. permtest1  AVotingCutOffNeutral=48.2
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffNeutral-48.2
-------------------+---------------------------------
 observations      | 12
  - positive       | 6
  - negative       | 6
  - zero           | 0
-------------------+---------------------------------
  critical value   | -8.834202194213901


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffNeutral>=48.2 : p = 
> .41259766
Test of hypothesis Ho: AVotingCutOffNeutral<=48.2 : p = 
> .58764648
Test of hypothesis Ho: AVotingCutOffNeutral==48.2 : p = 
> .82519531

. 
. 
. //////////      When the partisan bias is Supportive  
>     //////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVSupportive=mean(Wil
> lingness2Vote) if Supportive==1
(855 missing values generated)

. by ElectorateID, sort: egen AvergesSupportive=mean(Mea
> nWTVSupportive)

. by ElectorateID, sort: gen AVotingCutOffSupportive=Ave
> rgesSupportive if _n==1
(1,239 missing values generated)

. gen QualityTreatmentSupp=1

. mean AVotingCutOffSupportive

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> -----------------
                        |       Mean   Std. Err.     [95
> % Con                                                 
>      f. Interval]
------------------------+-------------------------------
> -----------------
AVotingCutOffSupportive |   21.72267   3.187422       14
> .7072                                                 
>          28.73813
--------------------------------------------------------
> -----------------

. 
. signrank  AVotingCutOffSupportive=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |       12          78          39
    negative |        0           0          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffSupportive = 0
             z =   3.059
    Prob > |z| =   0.0022

. permtest1  AVotingCutOffSupportive=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffSupportive-0
-------------------+---------------------------------
 observations      | 12
  - positive       | 12
  - negative       | 0
  - zero           | 0
-------------------+---------------------------------
  critical value   | 260.6719813346863


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffSupportive>=0 : p = 
> 1
Test of hypothesis Ho: AVotingCutOffSupportive<=0 : p = 
> .00024414
Test of hypothesis Ho: AVotingCutOffSupportive==0 : p = 
> .00048828

. 
. restore

. 
. 
. //////////////////////////////////////////////////////
> ////////////////////
> ////////////////                Figure 7              
>    /////////////////
> //////////////////////////////////////////////////////
> ////////////////////
> preserve

. //Based on the information elicted above, we make Figu
> re 7 using the following codes//
. 
. clear

. import excel "D:\FiguresReplications.xlsx",  sheet("Fi
> gure7WTV") firstrow

. twoway (bar Mean Position if Treatment=="Control"&Cate
> gory=="Supportive",  name(Supportive,replace) fcolor(b
> lack) bcolor(gs10) lwidth(0.1) xaxis(1 2) yaxis(1 2) )
> ||(bar Mean Position if Treatment=="T1"&Category=="Sup
> portive",  fcolor(gs2) bcolor(gs10) lwidth(0.1))||(bar
>  Mean Position if Treatment=="T2"&Category=="Supportiv
> e",  fcolor(gs7) bcolor(gs10) lwidth(0.1))||(bar Mean 
> Position if Treatment=="T3"&Category=="Supportive",  f
> color(gs10) bcolor(gs10) lwidth(0.1))||(bar Mean Posit
> ion if Treatment=="T4"&Category=="Supportive",  fcolor
> (gs14) bcolor(gs10) lwidth(0.1))||(bar Mean Position i
> f Treatment=="T5"&Category=="Supportive",  fcolor(whit
> e) bcolor(gs10) lwidth(0.1))||(scatter Prediction Posi
> tion if Category=="Supportive",mcolor(blue) msymbol(Sh
> )),  ylabel(0 (20) 100,nogrid) ylabel("",axis(2)) xlab
> el("") xlabel("",axis(2)) ytitle("Willingness to vote"
> ) ytitle("",axis(2)) xtitle("") xtitle("",axis(2))    
>  legend(region(lcolor(white))  order(1 2 3 4 5 6 ) rin
> g(0) position(1) symxsize(Medium) keygap(tiny)  col(1)
>  label(1 "Control (Mean)") label(2 "Treatment,N=2") la
> bel(3 "Treatment,N=3") label(4 "Treatment,N=4") label(
> 5 "Treatment,N=5")  label(6 "Optimal Cutoff Cost")) ti
> tle("Supportive",color(black))  graphregion(color(whit
> e)) plotregion(color(white))    
(note:  named style Medium not found in class gsize,
    default attributes used)

. twoway (bar Mean Position if Treatment=="Control"&Cate
> gory=="Neutral",  name(Neutral,replace) fcolor(black) 
> bcolor(gs10) lwidth(0.1) xaxis(1 2) yaxis(1 2) )||(bar
>  Mean Position if Treatment=="T1"&Category=="Neutral",
>   fcolor(gs2) bcolor(gs10) lwidth(0.1))||(bar Mean Pos
> ition if Treatment=="T2"&Category=="Neutral",  fcolor(
> gs7) bcolor(gs10) lwidth(0.1))||(bar Mean Position if 
> Treatment=="T3"&Category=="Neutral",  fcolor(gs10) bco
> lor(gs10) lwidth(0.1))||(bar Mean Position if Treatmen
> t=="T4"&Category=="Neutral",  fcolor(gs14) bcolor(gs10
> ) lwidth(0.1))||(bar Mean Position if Treatment=="T5"&
> Category=="Neutral",  fcolor(white) bcolor(gs10) lwidt
> h(0.1))||(scatter Prediction Position if Category=="Ne
> utral",mcolor(blue) msymbol(Sh)),  ylabel(0 (20) 100,n
> ogrid) ylabel("",axis(2)) xlabel("") xlabel("",axis(2)
> ) ytitle("Willingness to vote") ytitle("",axis(2)) xti
> tle("") xtitle("",axis(2))     legend(region(lcolor(wh
> ite))  order(1 2 3 4 5 6 ) ring(0) position(1) symxsiz
> e(Medium) keygap(tiny)  col(1) label(1 "Control (Mean)
> ") label(2 "Treatment,N=2") label(3 "Treatment,N=3") l
> abel(4 "Treatment,N=4") label(5 "Treatment,N=5")  labe
> l(6 "Optimal Cutoff Cost")) title("Neutral",color(blac
> k))  graphregion(color(white)) plotregion(color(white)
> )    
(note:  named style Medium not found in class gsize,
    default attributes used)

. twoway (bar Mean Position if Treatment=="Control"&Cate
> gory=="Against",  name(Against,replace) fcolor(black) 
> bcolor(gs10) lwidth(0.1) xaxis(1 2) yaxis(1 2) )||(bar
>  Mean Position if Treatment=="T1"&Category=="Against",
>   fcolor(gs2) bcolor(gs10) lwidth(0.1))||(bar Mean Pos
> ition if Treatment=="T2"&Category=="Against",  fcolor(
> gs7) bcolor(gs10) lwidth(0.1))||(bar Mean Position if 
> Treatment=="T3"&Category=="Against",  fcolor(gs10) bco
> lor(gs10) lwidth(0.1))||(bar Mean Position if Treatmen
> t=="T4"&Category=="Against",  fcolor(gs14) bcolor(gs10
> ) lwidth(0.1))||(bar Mean Position if Treatment=="T5"&
> Category=="Against",  fcolor(white) bcolor(gs10) lwidt
> h(0.1))||(scatter Prediction Position if Category=="Ag
> ainst",mcolor(blue) msymbol(Sh)),  ylabel(0 (20) 100,n
> ogrid) ylabel("",axis(2)) xlabel("") xlabel("",axis(2)
> ) ytitle("Willingness to vote") ytitle("",axis(2)) xti
> tle("") xtitle("",axis(2))     legend(region(lcolor(wh
> ite))  order(1 2 3 4 5 6 7) ring(0) position(1) symxsi
> ze(3) keygap(tiny)  col(4) label(1 "Control Group") la
> bel(2 "Treatment,N=1") label(3 "Treatment,N=2") label(
> 4 "Treatment,N=3") label(5 "Treatment,N=4") label(6 "T
> reatment,N=5") label(7 "Planner's Prescription") size(
> 2)) title("Against",color(black))  graphregion(color(w
> hite)) plotregion(color(white))    

. 
. 
. clear

. import excel "D:\FiguresReplications.xlsx",  sheet("Fi
> gure7Quality") firstrow

. twoway (bar Mean Position if Treatment=="Control"&Cate
> gory=="Supportive",  name(Supportive1,replace) fcolor(
> black) bcolor(gs10) lwidth(0.1) xaxis(1 2) yaxis(1 2) 
> )||(bar Mean Position if Treatment=="T1"&Category=="Su
> pportive",  fcolor(gs2) bcolor(gs10) lwidth(0.1))||(ba
> r Mean Position if Treatment=="T2"&Category=="Supporti
> ve",  fcolor(gs7) bcolor(gs10) lwidth(0.1))||(bar Mean
>  Position if Treatment=="T3"&Category=="Supportive",  
> fcolor(gs10) bcolor(gs10) lwidth(0.1))||(bar Mean Posi
> tion if Treatment=="T4"&Category=="Supportive",  fcolo
> r(gs14) bcolor(gs10) lwidth(0.1))||(bar Mean Position 
> if Treatment=="T5"&Category=="Supportive",  fcolor(whi
> te) bcolor(gs10) lwidth(0.1))||(scatter Prediction Pos
> ition if Category=="Supportive",mcolor(blue) msymbol(S
> h)),  ylabel(0 (0.2) 1,nogrid) ylabel("",axis(2)) xlab
> el("") xlabel("",axis(2)) ytitle("Quality of Democrati
> c Choice") ytitle("",axis(2)) xtitle("") xtitle("",axi
> s(2))     legend(region(lcolor(white))  order(1 2 3 4 
> 5 6 ) ring(0) position(1) symxsize(Medium) keygap(tiny
> )  col(1) label(1 "Control (Mean)") label(2 "Treatment
> ,N=2") label(3 "Treatment,N=3") label(4 "Treatment,N=4
> ") label(5 "Treatment,N=5")  label(6 "Optimal Cutoff C
> ost")) title("Supportive",color(black))  graphregion(c
> olor(white)) plotregion(color(white))    
(note:  named style Medium not found in class gsize,
    default attributes used)

. twoway (bar Mean Position if Treatment=="Control"&Cate
> gory=="Neutral",  name(Neutral1,replace) fcolor(black)
>  bcolor(gs10) lwidth(0.1) xaxis(1 2) yaxis(1 2) )||(ba
> r Mean Position if Treatment=="T1"&Category=="Neutral"
> ,  fcolor(gs2) bcolor(gs10) lwidth(0.1))||(bar Mean Po
> sition if Treatment=="T2"&Category=="Neutral",  fcolor
> (gs7) bcolor(gs10) lwidth(0.1))||(bar Mean Position if
>  Treatment=="T3"&Category=="Neutral",  fcolor(gs10) bc
> olor(gs10) lwidth(0.1))||(bar Mean Position if Treatme
> nt=="T4"&Category=="Neutral",  fcolor(gs14) bcolor(gs1
> 0) lwidth(0.1))||(bar Mean Position if Treatment=="T5"
> &Category=="Neutral",  fcolor(white) bcolor(gs10) lwid
> th(0.1))||(scatter Prediction Position if Category=="N
> eutral",mcolor(blue) msymbol(Sh)),  ylabel(0 (0.2) 1,n
> ogrid) ylabel("",axis(2)) xlabel("") xlabel("",axis(2)
> ) ytitle("Quality of Democratic Choice") ytitle("",axi
> s(2)) xtitle("") xtitle("",axis(2))     legend(region(
> lcolor(white))  order(1 2 3 4 5 6 ) ring(0) position(1
> ) symxsize(Medium) keygap(tiny)  col(1) label(1 "Contr
> ol (Mean)") label(2 "Treatment,N=2") label(3 "Treatmen
> t,N=3") label(4 "Treatment,N=4") label(5 "Treatment,N=
> 5")  label(6 "Optimal Cutoff Cost")) title("Neutral",c
> olor(black))  graphregion(color(white)) plotregion(col
> or(white))    
(note:  named style Medium not found in class gsize,
    default attributes used)

. twoway (bar Mean Position if Treatment=="Control"&Cate
> gory=="Against",  name(Against1,replace) fcolor(black)
>  bcolor(gs10) lwidth(0.1) xaxis(1 2) yaxis(1 2) )||(ba
> r Mean Position if Treatment=="T1"&Category=="Against"
> ,  fcolor(gs2) bcolor(gs10) lwidth(0.1))||(bar Mean Po
> sition if Treatment=="T2"&Category=="Against",  fcolor
> (gs7) bcolor(gs10) lwidth(0.1))||(bar Mean Position if
>  Treatment=="T3"&Category=="Against",  fcolor(gs10) bc
> olor(gs10) lwidth(0.1))||(bar Mean Position if Treatme
> nt=="T4"&Category=="Against",  fcolor(gs14) bcolor(gs1
> 0) lwidth(0.1))||(bar Mean Position if Treatment=="T5"
> &Category=="Against",  fcolor(white) bcolor(gs10) lwid
> th(0.1))||(scatter Prediction Position if Category=="A
> gainst",mcolor(blue) msymbol(Sh)),  ylabel(0 (0.2) 1,n
> ogrid) ylabel("",axis(2)) xlabel("") xlabel("",axis(2)
> ) ytitle("Quality of Democratic Choice") ytitle("",axi
> s(2)) xtitle("") xtitle("",axis(2))     legend(region(
> lcolor(white))  order(1 2 3 4 5 6 ) ring(0) position(1
> ) symxsize(Medium) keygap(tiny)  col(5) label(1 "Contr
> ol Group") label(2 "Treatment,N=2") label(3 "Treatment
> ,N=3") label(4 "Treatment,N=4") label(5 "Treatment,N=5
> ")  label(6 "Optimal Cutoff Cost")) title("Against",co
> lor(black))  graphregion(color(white)) plotregion(colo
> r(white))    
(note:  named style Medium not found in class gsize,
    default attributes used)

. grc1leg Against Neutral Supportive Against1 Neutral1 S
> upportive1, name(Figure7,replace) col(3) graphregion(c
> olor(white)) plotregion(color(white)) position(6) ring
> (1) note("Note: The vertical axis of figures in the fi
> rst row shows the willingness to vote. The vertical ax
> is of figures" "in the second row shows the quality of
>  democratic choice.")
(note:  named style Medium not found in class gsize,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)

. graph display Figure7, xsize(8) ysize(6)

. graph export "D:\Figure7.pdf", as(pdf) replace
(file D:\Figure7.pdf written in PDF format)

. restore

. 
. 
. 
. ******************************************************
> **************************
. ******************************************************
> **************************
. ******************************************************
> **************************
. 
. 
. //In the following, we report the statistical analysis
> , figures, and tables of Online Appendix//
. //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> /////////                Online Appendix A            
>         ////////
> //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> preserve

. tab State

      State |      Freq.     Percent        Cum.
------------+-----------------------------------
          1 |      1,805       50.14       50.14
          2 |      1,795       49.86      100.00
------------+-----------------------------------
      Total |      3,600      100.00

. tab Expertise

  Expertise |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |      1,089       30.25       30.25
          1 |      2,511       69.75      100.00
------------+-----------------------------------
      Total |      3,600      100.00

. tab Supportive if Treatment=="ControlGroup"

 Supportive |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |      1,225       68.06       68.06
          1 |        575       31.94      100.00
------------+-----------------------------------
      Total |      1,800      100.00

. tab Neutral if Treatment=="ControlGroup"

    Neutral |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |      1,220       67.78       67.78
          1 |        580       32.22      100.00
------------+-----------------------------------
      Total |      1,800      100.00

. tab Against if Treatment=="ControlGroup"

    Against |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |      1,155       64.17       64.17
          1 |        645       35.83      100.00
------------+-----------------------------------
      Total |      1,800      100.00

. tab Supportive if Treatment=="TreatmentGroup"

 Supportive |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |      1,210       67.22       67.22
          1 |        590       32.78      100.00
------------+-----------------------------------
      Total |      1,800      100.00

. tab Neutral if Treatment=="TreatmentGroup"

    Neutral |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |      1,200       66.67       66.67
          1 |        600       33.33      100.00
------------+-----------------------------------
      Total |      1,800      100.00

. tab Against if Treatment=="TreatmentGroup"

    Against |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |      1,190       66.11       66.11
          1 |        610       33.89      100.00
------------+-----------------------------------
      Total |      1,800      100.00

. restore

. //////////////////////////////////////////////////////
> ////////////////////
> ////////////////                Figure A1             
>     /////////////////
> //////////////////////////////////////////////////////
> ////////////////////
> preserve

. by ElectionID, sort: egen Informedness=mean(Expertise)

. gen SocialKnowledge=0

. replace SocialKnowledge=1 if Treatment=="TreatmentGrou
> p"
(1,800 real changes made)

. collapse Expertise Period SocialKnowledge Informedness
> ,by(ElectionID)

. by SocialKnowledge Period, sort: egen Informed=mean(In
> formedness) 

. by SocialKnowledge Period, sort: egen InformedSD=sd(In
> formedness) 

. collapse Informed InformedSD,by(SocialKnowledge Period
> )

. gen SE=InformedSD/(sqrt(6))

. gen Low95CI=Informed-1.96*SE

. gen High95CI=Informed+1.96*SE

. tw (rspike High95CI Low95CI Period if SocialKnowledge=
> =1, lcolor(gs12) xaxis(1 2) yaxis(1 2))||(scatter Info
> rmed Period if SocialKnowledge==1,name(withSK,replace)
>  mcolor(gs6)), graphregion(color(white)) plotregion(co
> lor(white)) bgcolor(white)  ylabel(0 0.5 0.7 1,nogrid)
>  ylabel("",axis(2)) xlabel("",axis(2)) ytitle("") xtit
> le("Period",axis(1)) xtitle("",axis(2)) title("Treatme
> nt Group",color(black)) legend(region(lcolor(white)) s
> ymxsize(Medium) keygap(tiny)order (2 1) label (2 "Mean
> ") label( 1 "95% CI") col(2) position (6) ring(0))  yl
> ine(0.7)
(note:  named style Medium not found in class gsize,
    default attributes used)

. tw (rspike High95CI Low95CI Period if SocialKnowledge=
> =0, lcolor(gs12) xaxis(1 2) yaxis(1 2))||(scatter Info
> rmed Period if SocialKnowledge==0,name(withoutSK,repla
> ce) mcolor(gs6)), graphregion(color(white)) plotregion
> (color(white)) bgcolor(white)  ylabel(0 0.5 0.7 1,nogr
> id) ylabel("",axis(2)) xlabel("",axis(2)) ytitle("") x
> title("Period",axis(1)) xtitle("",axis(2)) title("Cont
> rol Group",color(black)) legend(region(lcolor(white)) 
> symxsize(Medium) keygap(tiny)order (2 1) label (2 "Mea
> n") label( 1 "95% CI") col(2) position (6) ring(0))  y
> line(0.7)
(note:  named style Medium not found in class gsize,
    default attributes used)

. grc1leg withoutSK withSK, name(FigureA1,replace) l1("P
> roportion of Expert Voters") graphregion(color(white))
>  plotregion(color(white)) row(2)
(note:  named style Medium not found in class gsize,
    default attributes used)
(note:  named style Medium not found in class gsize,
    default attributes used)

. graph display FigureA1, xsize(12) ysize(8)

. graph export "D:\FigureA1.pdf", as(pdf) replace
(file D:\FigureA1.pdf written in PDF format)

. restore

. 
. //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> /////////                Online Appendix B            
>         ////////
> //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> preserve

. *First, we calculate the quality of democratic choice 
> in each election period
. gen RightChoice=0 if Expertise==1&Vote!=State&Willingn
> ess2Vote>=RandVotingCost
(3,591 missing values generated)

. replace RightChoice=1 if Vote==State&Expertise==1&Will
> ingness2Vote>=RandVotingCost
(760 real changes made)

. gen WrongChoice=0 if Expertise==1&Vote==State&Willingn
> ess2Vote>=RandVotingCost
(2,840 missing values generated)

. replace WrongChoice=1 if Vote!=State&Vote<3&Expertise=
> =1&Willingness2Vote>=RandVotingCost
(9 real changes made)

. by ElectionID, sort: egen NRightChoice=total(RightChoi
> ce)

. by ElectionID, sort: egen NWrongChoice=total(WrongChoi
> ce)

. gen SumRightVotes=NRightChoice+2 if Supportive==1
(2,435 missing values generated)

. replace SumRightVotes=NRightChoice+1 if Neutral==1
(1,180 real changes made)

. replace SumRightVotes=NRightChoice if Against==1
(1,255 real changes made)

. gen SumWrongVotes=NWrongChoice+2 if Against==1
(2,345 missing values generated)

. replace SumWrongVotes=NWrongChoice+1 if Neutral==1
(1,180 real changes made)

. replace SumWrongVotes=NWrongChoice if Supportive==1
(1,165 real changes made)

. gen ProbRight=1 if SumRightVotes>SumWrongVotes
(1,395 missing values generated)

. replace ProbRight=0 if SumRightVotes<SumWrongVotes
(760 real changes made)

. replace ProbRight=0.5 if SumRightVotes==SumWrongVotes
(635 real changes made)

. sort ElectionID

. by ElectionID: gen Quality=ProbRight if _n==1
(2,880 missing values generated)

. 
. //////////////////////////////////////////////////////
> ////////////////
> /////////                     Table A1                
>         ////////
> //////////////////////////////////////////////////////
> ////////////////
> //Then we run OLS regressions to check if the quality 
> of democratic choice significantly changes over time//
>  
. gen TreatmentDummy=0

. replace TreatmentDummy=1 if Treatment=="TreatmentGroup
> "
(1,800 real changes made)

. reg Quality TreatmentDummy,cluster(ElectorateID)

Linear regression                               Number o
> f obs     =        720
                                                F(1, 23)
>           =       6.54
                                                Prob > F
>           =     0.0176
                                                R-square
> d         =     0.0220
                                                Root MSE
>           =     .40302

                          (Std. Err. adjusted for 24 clu
> sters in ElectorateID)
--------------------------------------------------------
> ----------------------
             |               Robust
     Quality |      Coef.   Std. Err.      t    P>|t|   
>   [95% Con                                            
>           f. Interval]
-------------+------------------------------------------
> ----------------------
TreatmentD~y |  -.1208333   .0472498    -2.56   0.018   
>  -.2185769                                            
>              -.0230898
       _cons |   .7611111    .031256    24.35   0.000   
>   .6964532                                            
>                .825769
--------------------------------------------------------
> ----------------------

. outreg2 using Table_A1.doc,  replace  dec(3) alpha(0.0
> 1, 0.05, 0.10) symbol(***,**,*)
Table_A1.doc
dir : seeout

. reg Quality TreatmentDummy Period,cluster(ElectorateID
> )

Linear regression                               Number o
> f obs     =        720
                                                F(2, 23)
>           =       3.27
                                                Prob > F
>           =     0.0563
                                                R-square
> d         =     0.0221
                                                Root MSE
>           =     .40329

                          (Std. Err. adjusted for 24 clu
> sters in ElectorateID)
--------------------------------------------------------
> ----------------------
             |               Robust
     Quality |      Coef.   Std. Err.      t    P>|t|   
>   [95% Con                                            
>           f. Interval]
-------------+------------------------------------------
> ----------------------
TreatmentD~y |  -.1208333   .0472827    -2.56   0.018   
>  -.2186451                                            
>              -.0230216
      Period |   .0003754   .0021472     0.17   0.863   
>  -.0040665                                            
>               .0048173
       _cons |   .7552921    .045566    16.58   0.000   
>   .6610316                                            
>               .8495527
--------------------------------------------------------
> ----------------------

. outreg2 using Table_A1.doc,  append  dec(3) alpha(0.01
> , 0.05, 0.10) symbol(***,**,*)
Table_A1.doc
dir : seeout

. 
. //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> /////////                Online Appendix C            
>         ////////
> //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> /////////                     Table A2                
>         ////////
> //////////////////////////////////////////////////////
> ////////////////
> gen TreatmentAgainst=TreatmentDummy*Against

. gen TreatmentNeutral=TreatmentDummy*Neutral

. 
. reg Willingness2Vote Expertise,cluster(GlobalSubjectID
> )

Linear regression                               Number o
> f obs     =      3,600
                                                F(1, 119
> )         =     399.65
                                                Prob > F
>           =     0.0000
                                                R-square
> d         =     0.2271
                                                Root MSE
>           =      26.25

                      (Std. Err. adjusted for 120 cluste
> rs in GlobalSubjectID)
--------------------------------------------------------
> ----------------------
             |               Robust
Willingnes~e |      Coef.   Std. Err.      t    P>|t|   
>   [95% Con                                            
>           f. Interval]
-------------+------------------------------------------
> ----------------------
   Expertise |   30.96603   1.548986    19.99   0.000   
>   27.89888                                            
>               34.03318
       _cons |   1.634527   .3984897     4.10   0.000   
>   .8454777                                            
>               2.423576
--------------------------------------------------------
> ----------------------

. outreg2 using TableA2.doc,  replace  dec(3) alpha(0.01
> , 0.05, 0.10) symbol(***,**,*)
TableA2.doc
dir : seeout

. reg Willingness2Vote TreatmentDummy if Expertise==1,cl
> uster(GlobalSubjectID)

Linear regression                               Number o
> f obs     =      2,511
                                                F(1, 119
> )         =      28.34
                                                Prob > F
>           =     0.0000
                                                R-square
> d         =     0.0621
                                                Root MSE
>           =     29.974

                      (Std. Err. adjusted for 120 cluste
> rs in GlobalSubjectID)
--------------------------------------------------------
> ----------------------
             |               Robust
Willingnes~e |      Coef.   Std. Err.      t    P>|t|   
>   [95% Con                                            
>           f. Interval]
-------------+------------------------------------------
> ----------------------
TreatmentD~y |  -15.42147   2.896968    -5.32   0.000   
>  -21.15776                                            
>              -9.685182
       _cons |   40.33893   2.359575    17.10   0.000   
>   35.66674                                            
>               45.01112
--------------------------------------------------------
> ----------------------

. outreg2 using TableA2.doc,  append  dec(3) alpha(0.01,
>  0.05, 0.10) symbol(***,**,*)
TableA2.doc
dir : seeout

. reg Willingness2Vote Period if Expertise==1,cluster(Gl
> obalSubjectID)

Linear regression                               Number o
> f obs     =      2,511
                                                F(1, 119
> )         =       0.33
                                                Prob > F
>           =     0.5656
                                                R-square
> d         =     0.0002
                                                Root MSE
>           =     30.948

                      (Std. Err. adjusted for 120 cluste
> rs in GlobalSubjectID)
--------------------------------------------------------
> ----------------------
             |               Robust
Willingnes~e |      Coef.   Std. Err.      t    P>|t|   
>   [95% Con                                            
>           f. Interval]
-------------+------------------------------------------
> ----------------------
      Period |    -.04502    .078133    -0.58   0.566   
>  -.1997311                                            
>               .1096911
       _cons |   33.30029   1.935296    17.21   0.000   
>   29.46821                                            
>               37.13238
--------------------------------------------------------
> ----------------------

. outreg2 using TableA2.doc,  append  dec(3) alpha(0.01,
>  0.05, 0.10) symbol(***,**,*)
TableA2.doc
dir : seeout

. reg Willingness2Vote Against Neutral if Expertise==1,c
> luster(GlobalSubjectID)

Linear regression                               Number o
> f obs     =      2,511
                                                F(2, 119
> )         =      53.12
                                                Prob > F
>           =     0.0000
                                                R-square
> d         =     0.1197
                                                Root MSE
>           =     29.045

                      (Std. Err. adjusted for 120 cluste
> rs in GlobalSubjectID)
--------------------------------------------------------
> ----------------------
             |               Robust
Willingnes~e |      Coef.   Std. Err.      t    P>|t|   
>   [95% Con                                            
>           f. Interval]
-------------+------------------------------------------
> ----------------------
     Against |   24.99072   2.480803    10.07   0.000   
>   20.07849                                            
>               29.90296
     Neutral |   19.64679   2.382723     8.25   0.000   
>   14.92876                                            
>               24.36482
       _cons |   17.39233   1.826483     9.52   0.000   
>   13.77571                                            
>               21.00895
--------------------------------------------------------
> ----------------------

. outreg2 using TableA2.doc,  append  dec(3) alpha(0.01,
>  0.05, 0.10) symbol(***,**,*)
TableA2.doc
dir : seeout

. reg Willingness2Vote TreatmentDummy Period Against Neu
> tral if Expertise==1,cluster(GlobalSubjectID)

Linear regression                               Number o
> f obs     =      2,511
                                                F(4, 119
> )         =      32.35
                                                Prob > F
>           =     0.0000
                                                R-square
> d         =     0.1788
                                                Root MSE
>           =     28.064

                      (Std. Err. adjusted for 120 cluste
> rs in GlobalSubjectID)
--------------------------------------------------------
> ----------------------
             |               Robust
Willingnes~e |      Coef.   Std. Err.      t    P>|t|   
>   [95% Con                                            
>           f. Interval]
-------------+------------------------------------------
> ----------------------
TreatmentD~y |  -15.04924   2.876425    -5.23   0.000   
>  -20.74485                                            
>              -9.353632
      Period |   .0171889   .0744179     0.23   0.818   
>   -.130166                                            
>               .1645438
     Against |   24.51608    2.45617     9.98   0.000   
>   19.65262                                            
>               29.37955
     Neutral |   19.81336   2.330063     8.50   0.000   
>    15.1996                                            
>               24.42712
       _cons |   24.78978    2.76778     8.96   0.000   
>    19.3093                                            
>               30.27026
--------------------------------------------------------
> ----------------------

. outreg2 using TableA2.doc,  append  dec(3) alpha(0.01,
>  0.05, 0.10) symbol(***,**,*)
TableA2.doc
dir : seeout

. reg Willingness2Vote TreatmentDummy Period Against Neu
> tral TreatmentAgainst TreatmentNeutral if Expertise==1
> ,cluster(GlobalSubjectID)

Linear regression                               Number o
> f obs     =      2,511
                                                F(6, 119
> )         =      24.78
                                                Prob > F
>           =     0.0000
                                                R-square
> d         =     0.1857
                                                Root MSE
>           =     27.956

                      (Std. Err. adjusted for 120 cluste
> rs in GlobalSubjectID)
--------------------------------------------------------
> ----------------------
             |               Robust
Willingnes~e |      Coef.   Std. Err.      t    P>|t|   
>   [95% Con                                            
>           f. Interval]
-------------+------------------------------------------
> ----------------------
TreatmentD~y |   -7.60667     3.6232    -2.10   0.038   
>  -14.78097                                            
>              -.4323719
      Period |   .0312015   .0732686     0.43   0.671   
>  -.1138776                                            
>               .1762807
     Against |   30.32327   3.877744     7.82   0.000   
>   22.64495                                            
>               38.00159
     Neutral |   25.08883   4.224111     5.94   0.000   
>   16.72467                                            
>               33.45299
TreatmentA~t |  -11.62325   4.804657    -2.42   0.017   
>  -21.13695                                            
>              -2.109549
TreatmentN~l |  -10.28101   4.666259    -2.20   0.030   
>  -19.52066                                            
>              -1.041347
       _cons |   20.76967   3.252378     6.39   0.000   
>   14.32963                                            
>                27.2097
--------------------------------------------------------
> ----------------------

. outreg2 using TableA2.doc,  append  dec(3) alpha(0.01,
>  0.05, 0.10) symbol(***,**,*)
TableA2.doc
dir : seeout

. reg Willingness2Vote TreatmentDummy Period Against Neu
> tral TreatmentAgainst TreatmentNeutral Age Female CRTS
> core if Expertise==1,cluster(GlobalSubjectID)

Linear regression                               Number o
> f obs     =      2,511
                                                F(9, 119
> )         =      17.71
                                                Prob > F
>           =     0.0000
                                                R-square
> d         =     0.1909
                                                Root MSE
>           =     27.884

                      (Std. Err. adjusted for 120 cluste
> rs in GlobalSubjectID)
--------------------------------------------------------
> ----------------------
             |               Robust
Willingnes~e |      Coef.   Std. Err.      t    P>|t|   
>   [95% Con                                            
>           f. Interval]
-------------+------------------------------------------
> ----------------------
TreatmentD~y |  -8.120827   3.652604    -2.22   0.028   
>  -15.35335                                            
>              -.8883055
      Period |   .0310014   .0732168     0.42   0.673   
>  -.1139751                                            
>               .1759778
     Against |    30.1638   3.883259     7.77   0.000   
>   22.47456                                            
>               37.85304
     Neutral |    25.2342   4.254899     5.93   0.000   
>   16.80907                                            
>               33.65932
TreatmentA~t |  -11.14117   4.812307    -2.32   0.022   
>  -20.67001                                            
>              -1.612318
TreatmentN~l |  -10.28933   4.704782    -2.19   0.031   
>  -19.60527                                            
>              -.9733933
         Age |  -.5209916   .3236375    -1.61   0.110   
>  -1.161826                                            
>                .119843
      Female |  -1.852446    2.89173    -0.64   0.523   
>   -7.57836                                            
>               3.873467
    CRTScore |  -.4719708   1.205904    -0.39   0.696   
>  -2.859781                                            
>                1.91584
       _cons |   32.97244   8.200935     4.02   0.000   
>   16.73377                                            
>               49.21111
--------------------------------------------------------
> ----------------------

. outreg2 using TableA2.doc,  append  dec(3) alpha(0.01,
>  0.05, 0.10) symbol(***,**,*)
TableA2.doc
dir : seeout

. 
. //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> /////////                Online Appendix D            
>         ////////
> //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> /////////                     Table A3                
>         ////////
> //////////////////////////////////////////////////////
> ////////////////
> reg Quality Period if Treatment=="ControlGroup",cluste
> r(ElectorateID)

Linear regression                               Number o
> f obs     =        360
                                                F(1, 11)
>           =       0.50
                                                Prob > F
>           =     0.4947
                                                R-square
> d         =     0.0019
                                                Root MSE
>           =     .37876

                          (Std. Err. adjusted for 12 clu
> sters in ElectorateID)
--------------------------------------------------------
> ----------------------
             |               Robust
     Quality |      Coef.   Std. Err.      t    P>|t|   
>   [95% Con                                            
>           f. Interval]
-------------+------------------------------------------
> ----------------------
      Period |   .0019095   .0027036     0.71   0.495   
>   -.004041                                            
>               .0078601
       _cons |   .7315134   .0525213    13.93   0.000   
>   .6159148                                            
>                .847112
--------------------------------------------------------
> ----------------------

. outreg2 using TableA3.doc,  replace  dec(3) alpha(0.01
> , 0.05, 0.10) symbol(***,**,*)
TableA3.doc
dir : seeout

. reg Quality Period if Treatment=="TreatmentGroup",clus
> ter(ElectorateID)

Linear regression                               Number o
> f obs     =        360
                                                F(1, 11)
>           =       0.12
                                                Prob > F
>           =     0.7395
                                                R-square
> d         =     0.0006
                                                Root MSE
>           =     .42653

                          (Std. Err. adjusted for 12 clu
> sters in ElectorateID)
--------------------------------------------------------
> ----------------------
             |               Robust
     Quality |      Coef.   Std. Err.      t    P>|t|   
>   [95% Con                                            
>           f. Interval]
-------------+------------------------------------------
> ----------------------
      Period |  -.0011587   .0033974    -0.34   0.739   
>  -.0086364                                            
>                .006319
       _cons |   .6582375   .0687164     9.58   0.000   
>   .5069938                                            
>               .8094813
--------------------------------------------------------
> ----------------------

. outreg2 using TableA3.doc,  append  dec(3) alpha(0.01,
>  0.05, 0.10) symbol(***,**,*)
TableA3.doc
dir : seeout

. restore

. 
. 
. //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> /////////                Online Appendix G            
>         ////////
> //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> /////////                     Table A4                
>         ////////
> //////////////////////////////////////////////////////
> ////////////////
> //In Table A4, we report theoretical analysis of Pivot
> al Voting Models//
. //The equilibrium point predictions and how they are c
> alculated and detailed in Online Appendix G//
. //Specifically, the point predictions for Against when
>  Expertise is Unknown is 27.55, 
. //which is reported on page 16 of Online Appendix.
. //The point predictions for Against and Supportive whe
> n Expertise is Unknown is 23.98 and 0, respectively, 
. //which is reported on page 17 of Online Appendix.
. //The point predictions for the average willingness to
>  vote when Expertise is Unknown is 17.18, 
. //which is reported on page 17 of Online Appendix.
. //When Expertise is Known, when the partisan bias is A
> gainst, the point predictions are 
. //reported by the number of realized expert voters on 
> page 18 of Online Appendix.
. //When Expertise is Known, when the partisan bias is N
> eutral or Supportive, the point predictions are 
. //reported by the number of realized expert voters on 
> page 19 of Online Appendix.
. //The point predictions for the average willingness to
>  vote when Expertise is Known is 7.78, 
. //which is reported on page 20 of Online Appendix.
. 
. //The experimental results are based on the statistics
>  derived by this do file, and copied from Lines 600-78
> 7
. preserve

. *We first focus on the behavior of expert voters in th
> e Treatment Group
. drop if Expertise==0
(1,089 observations deleted)

. drop if Treatment=="ControlGroup"
(1,251 observations deleted)

. 
. 
. /////////When Partisan Bias was Against and There was 
> 1 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVAgainst1=mean(Willi
> ngness2Vote) if Against==1&HowManyHaveExpertise==1
(1256 missing values generated)

. by ElectorateID, sort: egen AvergesAgainst1=mean(MeanW
> TVAgainst1)
(933 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffAgainst1=Averg
> esAgainst1 if _n==1
(1,257 missing values generated)

. gen QualityTreatmentAgaN1=0

. mean AVotingCutOffAgainst1

Mean estimation                   Number of obs   =     
>      3

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst1 |   5.833333   4.639804     -14.13
> 013                                                   
>         25.7968
--------------------------------------------------------
> ---------------

. mean QualityTreatmentAgaN1

Mean estimation                   Number of obs   =     
>  1,260

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentAgaN1 |          0  (omitted)
--------------------------------------------------------
> ---------------

. signrank  AVotingCutOffAgainst1=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        2           5         2.5
    negative |        0           0         2.5
        zero |        1           1           1
-------------+---------------------------------
         all |        3           6           6

unadjusted variance        3.50
adjustment for ties        0.00
adjustment for zeros      -0.25
                     ----------
adjusted variance          3.25

Ho: AVotingCutOffAgainst1 = 0
             z =   1.387
    Prob > |z| =   0.1655

. permtest1  AVotingCutOffAgainst1=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffAgainst1-0
-------------------+---------------------------------
 observations      | 3
  - positive       | 2
  - negative       | 0
  - zero           | 1
-------------------+---------------------------------
  critical value   | 17.5


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffAgainst1>=0 : p = 1
Test of hypothesis Ho: AVotingCutOffAgainst1<=0 : p = .2
> 5
Test of hypothesis Ho: AVotingCutOffAgainst1==0 : p = .5

. 
. /////////When Partisan Bias was Against and There were
>  2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVAgainst2=mean(Willi
> ngness2Vote) if Against==1&HowManyHaveExpertise==2
(1234 missing values generated)

. by ElectorateID, sort: egen AvergesAgainst2=mean(MeanW
> TVAgainst2)
(432 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffAgainst2=Averg
> esAgainst2 if _n==1
(1,252 missing values generated)

. gen QualityTreatmentAgaN2=(AVotingCutOffAgainst2/100)^
> 2
(1,252 missing values generated)

. mean AVotingCutOffAgainst2

Mean estimation                   Number of obs   =     
>      8

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst2 |   27.26042   6.667995      11.49
> 311                                                   
>        43.02772
--------------------------------------------------------
> ---------------

. mean QualityTreatmentAgaN2

Mean estimation                   Number of obs   =     
>      8

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentAgaN2 |   .1054365   .0337554      .0256
> 176                                                   
>        .1852555
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentAgaN2=1

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          18
    negative |        8          36          18
        zero |        0           0           0
-------------+---------------------------------
         all |        8          36          36

unadjusted variance       51.00
adjustment for ties       -0.13
adjustment for zeros       0.00
                     ----------
adjusted variance         50.88

Ho: QualityTreatmentAgaN2 = 1
             z =  -2.524
    Prob > |z| =   0.0116

. permtest1 QualityTreatmentAgaN2=1
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentAgaN2-1
-------------------+---------------------------------
 observations      | 8
  - positive       | 0
  - negative       | 8
  - zero           | 0
-------------------+---------------------------------
  critical value   | -7.156507655819951


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentAgaN2>=1 : p = .0
> 0390625
Test of hypothesis Ho: QualityTreatmentAgaN2<=1 : p = 1
Test of hypothesis Ho: QualityTreatmentAgaN2==1 : p = .0
> 078125

. signrank  AVotingCutOffAgainst2=100

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          18
    negative |        8          36          18
        zero |        0           0           0
-------------+---------------------------------
         all |        8          36          36

unadjusted variance       51.00
adjustment for ties       -0.13
adjustment for zeros       0.00
                     ----------
adjusted variance         50.88

Ho: AVotingCutOffAgainst2 = 100
             z =  -2.524
    Prob > |z| =   0.0116

. permtest1  AVotingCutOffAgainst2=100
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffAgainst2-100
-------------------+---------------------------------
 observations      | 8
  - positive       | 0
  - negative       | 8
  - zero           | 0
-------------------+---------------------------------
  critical value   | -581.9166679382324


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffAgainst2>=100 : p = 
> .00390625
Test of hypothesis Ho: AVotingCutOffAgainst2<=100 : p = 
> 1
Test of hypothesis Ho: AVotingCutOffAgainst2==100 : p = 
> .0078125

. 
. /////////When Partisan Bias was Against and There were
>  3 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVAgainst3=mean(Willi
> ngness2Vote) if Against==1&HowManyHaveExpertise==3
(1140 missing values generated)

. by ElectorateID, sort: egen AvergesAgainst3=mean(MeanW
> TVAgainst3)
(112 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffAgainst3=Averg
> esAgainst3 if _n==1
(1,249 missing values generated)

. gen QualityTreatmentAgaN3=comb(3,3)*(AVotingCutOffAgai
> nst3/100)^3+0.5*comb(3,2)*((AVotingCutOffAgainst3/100)
> ^2)*(1-(AVotingCutOffAgainst3/100))
(1,249 missing values generated)

. mean AVotingCutOffAgainst3

Mean estimation                   Number of obs   =     
>     11

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst3 |   35.41306   3.641884      27.29
> 844                                                   
>        43.52768
--------------------------------------------------------
> ---------------

. mean QualityTreatmentAgaN3

Mean estimation                   Number of obs   =     
>     11

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentAgaN3 |   .1779707   .0354245        .09
> 904                                                   
>        .2569014
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentAgaN3=1

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          33
    negative |       11          66          33
        zero |        0           0           0
-------------+---------------------------------
         all |       11          66          66

unadjusted variance      126.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        126.50

Ho: QualityTreatmentAgaN3 = 1
             z =  -2.934
    Prob > |z| =   0.0033

. permtest1 QualityTreatmentAgaN3=1
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentAgaN3-1
-------------------+---------------------------------
 observations      | 11
  - positive       | 0
  - negative       | 11
  - zero           | 0
-------------------+---------------------------------
  critical value   | -9.042322549968958


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentAgaN3>=1 : p = .0
> 0048828
Test of hypothesis Ho: QualityTreatmentAgaN3<=1 : p = 1
Test of hypothesis Ho: QualityTreatmentAgaN3==1 : p = .0
> 0097656

. signrank  AVotingCutOffAgainst3=100

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          33
    negative |       11          66          33
        zero |        0           0           0
-------------+---------------------------------
         all |       11          66          66

unadjusted variance      126.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        126.50

Ho: AVotingCutOffAgainst3 = 100
             z =  -2.934
    Prob > |z| =   0.0033

. permtest1  AVotingCutOffAgainst3=100
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffAgainst3-100
-------------------+---------------------------------
 observations      | 11
  - positive       | 0
  - negative       | 11
  - zero           | 0
-------------------+---------------------------------
  critical value   | -710.4563522338867


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffAgainst3>=100 : p = 
> .00048828
Test of hypothesis Ho: AVotingCutOffAgainst3<=100 : p = 
> 1
Test of hypothesis Ho: AVotingCutOffAgainst3==100 : p = 
> .00097656

. 
. /////////When Partisan Bias was Against and There were
>  4 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVAgainst4=mean(Willi
> ngness2Vote) if Against==1&HowManyHaveExpertise==4
(1048 missing values generated)

. by ElectorateID, sort: egen AvergesAgainst4=mean(MeanW
> TVAgainst4)

. by ElectorateID, sort: gen AVotingCutOffAgainst4=Averg
> esAgainst4 if _n==1
(1,248 missing values generated)

. gen QualityTreatmentAgaN4=comb(4,3)*((AVotingCutOffAga
> inst4/100)^3)*(1-(AVotingCutOffAgainst4/100))+0.5*comb
> (4,2)*((AVotingCutOffAgainst4/100)^2)*(1-(AVotingCutOf
> fAgainst3/100)^2)
(1,249 missing values generated)

. mean AVotingCutOffAgainst4

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst4 |   34.32882   3.422976       26.7
> 949                                                   
>        41.86274
--------------------------------------------------------
> ---------------

. mean QualityTreatmentAgaN4

Mean estimation                   Number of obs   =     
>     11

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentAgaN4 |   .4638175   .1015254      .2376
> 048                                                   
>        .6900302
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentAgaN4=0.951638

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           2          33
    negative |       10          64          33
        zero |        0           0           0
-------------+---------------------------------
         all |       11          66          66

unadjusted variance      126.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        126.50

Ho: QualityTreatmentAgaN4 = 0.951638
             z =  -2.756
    Prob > |z| =   0.0058

. permtest1 QualityTreatmentAgaN4=0.951638
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentAgaN4-0.951638
-------------------+---------------------------------
 observations      | 11
  - positive       | 1
  - negative       | 10
  - zero           | 0
-------------------+---------------------------------
  critical value   | -5.366025221519946


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentAgaN4>=0.951638 :
>  p = .00146484
Test of hypothesis Ho: QualityTreatmentAgaN4<=0.951638 :
>  p = .99902344
Test of hypothesis Ho: QualityTreatmentAgaN4==0.951638 :
>  p = .00292969

. signrank  AVotingCutOffAgainst4=86.7

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          39
    negative |       12          78          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffAgainst4 = 86.7
             z =  -3.059
    Prob > |z| =   0.0022

. permtest1  AVotingCutOffAgainst4=86.7
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffAgainst4-86.7
-------------------+---------------------------------
 observations      | 12
  - positive       | 0
  - negative       | 12
  - zero           | 0
-------------------+---------------------------------
  critical value   | -628.4541667938233


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffAgainst4>=86.7 : p =
>  .00024414
Test of hypothesis Ho: AVotingCutOffAgainst4<=86.7 : p =
>  1
Test of hypothesis Ho: AVotingCutOffAgainst4==86.7 : p =
>  .00048828

. 
. /////////When Partisan Bias was Against and There were
>  5 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVAgainst5=mean(Willi
> ngness2Vote) if Against==1&HowManyHaveExpertise==5
(1200 missing values generated)

. by ElectorateID, sort: egen AvergesAgainst5=mean(MeanW
> TVAgainst5)
(416 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffAgainst5=Averg
> esAgainst5 if _n==1
(1,252 missing values generated)

. gen QualityTreatmentAgaN5=comb(5,3)*((AVotingCutOffAga
> inst5/100)^3)*(1-(AVotingCutOffAgainst4/100))^2+0.5*co
> mb(5,2)*((AVotingCutOffAgainst5/100)^2)*(1-(AVotingCut
> OffAgainst3/100)^5)
(1,253 missing values generated)

. mean AVotingCutOffAgainst5

Mean estimation                   Number of obs   =     
>      8

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst5 |    29.6875   4.147264      19.88
> 078                                                   
>        39.49422
--------------------------------------------------------
> ---------------

. mean QualityTreatmentAgaN5

Mean estimation                   Number of obs   =     
>      7

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentAgaN5 |   .6443061   .1963658      .1638
> 163                                                   
>        1.124796
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentAgaN5=0.880517

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        2           8          14
    negative |        5          20          14
        zero |        0           0           0
-------------+---------------------------------
         all |        7          28          28

unadjusted variance       35.00
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         35.00

Ho: QualityTreatmentAgaN5 = 0.880517
             z =  -1.014
    Prob > |z| =   0.3105

. permtest1 QualityTreatmentAgaN5=0.880517
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentAgaN5-0.880517
-------------------+---------------------------------
 observations      | 7
  - positive       | 2
  - negative       | 5
  - zero           | 0
-------------------+---------------------------------
  critical value   | -1.653476122302055


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentAgaN5>=0.880517 :
>  p = .15625
Test of hypothesis Ho: QualityTreatmentAgaN5<=0.880517 :
>  p = .8515625
Test of hypothesis Ho: QualityTreatmentAgaN5==0.880517 :
>  p = .3125

. signrank  AVotingCutOffAgainst5=67.5

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          18
    negative |        8          36          18
        zero |        0           0           0
-------------+---------------------------------
         all |        8          36          36

unadjusted variance       51.00
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         51.00

Ho: AVotingCutOffAgainst5 = 67.5
             z =  -2.521
    Prob > |z| =   0.0117

. permtest1  AVotingCutOffAgainst5=67.5
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffAgainst5-67.5
-------------------+---------------------------------
 observations      | 8
  - positive       | 0
  - negative       | 8
  - zero           | 0
-------------------+---------------------------------
  critical value   | -302.5


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffAgainst5>=67.5 : p =
>  .00390625
Test of hypothesis Ho: AVotingCutOffAgainst5<=67.5 : p =
>  1
Test of hypothesis Ho: AVotingCutOffAgainst5==67.5 : p =
>  .0078125

. 
. 
. /////////When Partisan Bias was Neutral and There was 
> 1 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVNeutral1=mean(Willi
> ngness2Vote) if Neutral==1&HowManyHaveExpertise==1
(1257 missing values generated)

. by ElectorateID, sort: egen AvergesNeutral1=mean(MeanW
> TVNeutral1)
(961 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffNeutral1=Averg
> esNeutral1 if _n==1
(1,257 missing values generated)

. gen QualityTreatmentNeuN1=1-0.5*(1-AVotingCutOffNeutra
> l1/100)
(1,257 missing values generated)

. mean AVotingCutOffNeutral1

Mean estimation                   Number of obs   =     
>      3

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral1 |   23.33333   14.52966     -39.18
> 276                                                   
>        85.84943
--------------------------------------------------------
> ---------------

. mean QualityTreatmentNeuN1

Mean estimation                   Number of obs   =     
>      3

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentNeuN1 |   .6166667   .0726483      .3040
> 862                                                   
>        .9292471
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentNeuN1=1

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0           3
    negative |        3           6           3
        zero |        0           0           0
-------------+---------------------------------
         all |        3           6           6

unadjusted variance        3.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance          3.50

Ho: QualityTreatmentNeuN1 = 1
             z =  -1.604
    Prob > |z| =   0.1088

. permtest1 QualityTreatmentNeuN1=1
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentNeuN1-1
-------------------+---------------------------------
 observations      | 3
  - positive       | 0
  - negative       | 3
  - zero           | 0
-------------------+---------------------------------
  critical value   | -1.149999976158142


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentNeuN1>=1 : p = .1
> 25
Test of hypothesis Ho: QualityTreatmentNeuN1<=1 : p = 1
Test of hypothesis Ho: QualityTreatmentNeuN1==1 : p = .2
> 5

. signrank  AVotingCutOffNeutral1=100

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0           3
    negative |        3           6           3
        zero |        0           0           0
-------------+---------------------------------
         all |        3           6           6

unadjusted variance        3.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance          3.50

Ho: AVotingCutOffNeutral1 = 100
             z =  -1.604
    Prob > |z| =   0.1088

. permtest1  AVotingCutOffNeutral1=100
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffNeutral1-100
-------------------+---------------------------------
 observations      | 3
  - positive       | 0
  - negative       | 3
  - zero           | 0
-------------------+---------------------------------
  critical value   | -230


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffNeutral1>=100 : p = 
> .125
Test of hypothesis Ho: AVotingCutOffNeutral1<=100 : p = 
> 1
Test of hypothesis Ho: AVotingCutOffNeutral1==100 : p = 
> .25

. 
. /////////When Partisan Bias was Neutral and There were
>  2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVNeutral2=mean(Willi
> ngness2Vote) if Neutral==1&HowManyHaveExpertise==2
(1232 missing values generated)

. by ElectorateID, sort: egen AvergesNeutral2=mean(MeanW
> TVNeutral2)
(325 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffNeutral2=Averg
> esNeutral2 if _n==1
(1,251 missing values generated)

. gen QualityTreatmentNeuN2=1-0.5*(1-AVotingCutOffNeutra
> l2/100)^2
(1,251 missing values generated)

. mean AVotingCutOffNeutral2

Mean estimation                   Number of obs   =     
>      9

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral2 |   31.16667   5.608928      18.23
> 246                                                   
>        44.10088
--------------------------------------------------------
> ---------------

. mean QualityTreatmentNeuN2

Mean estimation                   Number of obs   =     
>      9

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentNeuN2 |   .7505146   .0354732      .6687
> 133                                                   
>        .8323159
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentNeuN2=0.959184

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0        22.5
    negative |        9          45        22.5
        zero |        0           0           0
-------------+---------------------------------
         all |        9          45          45

unadjusted variance       71.25
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         71.25

Ho: QualityTreatmentNeuN2 = 0.959184
             z =  -2.666
    Prob > |z| =   0.0077

. permtest1 QualityTreatmentNeuN2=0.959184
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentNeuN2-0.959184
-------------------+---------------------------------
 observations      | 9
  - positive       | 0
  - negative       | 9
  - zero           | 0
-------------------+---------------------------------
  critical value   | -1.878024778705598


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentNeuN2>=0.959184 :
>  p = .00195313
Test of hypothesis Ho: QualityTreatmentNeuN2<=0.959184 :
>  p = 1
Test of hypothesis Ho: QualityTreatmentNeuN2==0.959184 :
>  p = .00390625

. signrank  AVotingCutOffNeutral2=71.4

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0        22.5
    negative |        9          45        22.5
        zero |        0           0           0
-------------+---------------------------------
         all |        9          45          45

unadjusted variance       71.25
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         71.25

Ho: AVotingCutOffNeutral2 = 71.4
             z =  -2.666
    Prob > |z| =   0.0077

. permtest1  AVotingCutOffNeutral2=71.4
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffNeutral2-71.4
-------------------+---------------------------------
 observations      | 9
  - positive       | 0
  - negative       | 9
  - zero           | 0
-------------------+---------------------------------
  critical value   | -362.1


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffNeutral2>=71.4 : p =
>  .00195313
Test of hypothesis Ho: AVotingCutOffNeutral2<=71.4 : p =
>  1
Test of hypothesis Ho: AVotingCutOffNeutral2==71.4 : p =
>  .00390625

. 
. /////////When Partisan Bias was Neutral and There were
>  3 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVNeutral3=mean(Willi
> ngness2Vote) if Neutral==1&HowManyHaveExpertise==3
(1146 missing values generated)

. by ElectorateID, sort: egen AvergesNeutral3=mean(MeanW
> TVNeutral3)

. by ElectorateID, sort: gen AVotingCutOffNeutral3=Averg
> esNeutral3 if _n==1
(1,248 missing values generated)

. gen QualityTreatmentNeuN3=1-0.5*(1-AVotingCutOffNeutra
> l3/100)^3
(1,248 missing values generated)

. mean AVotingCutOffNeutral3

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral3 |   29.35231   2.229159      24.44
> 597                                                   
>        34.25866
--------------------------------------------------------
> ---------------

. mean QualityTreatmentNeuN3

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentNeuN3 |   .8179367   .0167815      .7810
> 009                                                   
>        .8548725
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentNeuN3=0.950269

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          39
    negative |       12          78          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties       -0.13
adjustment for zeros       0.00
                     ----------
adjusted variance        162.38

Ho: QualityTreatmentNeuN3 = 0.950269
             z =  -3.061
    Prob > |z| =   0.0022

. permtest1 QualityTreatmentNeuN3=0.950269
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentNeuN3-0.950269
-------------------+---------------------------------
 observations      | 12
  - positive       | 0
  - negative       | 12
  - zero           | 0
-------------------+---------------------------------
  critical value   | -1.587987676456452


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentNeuN3>=0.950269 :
>  p = .00024414
Test of hypothesis Ho: QualityTreatmentNeuN3<=0.950269 :
>  p = 1
Test of hypothesis Ho: QualityTreatmentNeuN3==0.950269 :
>  p = .00048828

. signrank  AVotingCutOffNeutral3=53.7

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          39
    negative |       12          78          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties       -0.13
adjustment for zeros       0.00
                     ----------
adjusted variance        162.38

Ho: AVotingCutOffNeutral3 = 53.7
             z =  -3.061
    Prob > |z| =   0.0022

. permtest1  AVotingCutOffNeutral3=53.7
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffNeutral3-53.7
-------------------+---------------------------------
 observations      | 12
  - positive       | 0
  - negative       | 12
  - zero           | 0
-------------------+---------------------------------
  critical value   | -292.1722206115723


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffNeutral3>=53.7 : p =
>  .00024414
Test of hypothesis Ho: AVotingCutOffNeutral3<=53.7 : p =
>  1
Test of hypothesis Ho: AVotingCutOffNeutral3==53.7 : p =
>  .00048828

. 
. /////////When Partisan Bias was Neutral and There were
>  4 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVNeutral4=mean(Willi
> ngness2Vote) if Neutral==1&HowManyHaveExpertise==4
(1084 missing values generated)

. by ElectorateID, sort: egen AvergesNeutral4=mean(MeanW
> TVNeutral4)

. by ElectorateID, sort: gen AVotingCutOffNeutral4=Averg
> esNeutral4 if _n==1
(1,248 missing values generated)

. gen QualityTreatmentNeuN4=1-0.5*(1-AVotingCutOffNeutra
> l4/100)^4
(1,248 missing values generated)

. mean AVotingCutOffNeutral4

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral4 |   28.91771   2.884807      22.56
> 829                                                   
>        35.26713
--------------------------------------------------------
> ---------------

. mean QualityTreatmentNeuN4

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentNeuN4 |   .8585247   .0214247      .8113
> 691                                                   
>        .9056802
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentNeuN4=0.950828

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           1          39
    negative |       11          77          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: QualityTreatmentNeuN4 = 0.950828
             z =  -2.981
    Prob > |z| =   0.0029

. permtest1 QualityTreatmentNeuN4=0.950828
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentNeuN4-0.950828
-------------------+---------------------------------
 observations      | 12
  - positive       | 1
  - negative       | 11
  - zero           | 0
-------------------+---------------------------------
  critical value   | -1.107639838348388


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentNeuN4>=0.950828 :
>  p = .00048828
Test of hypothesis Ho: QualityTreatmentNeuN4<=0.950828 :
>  p = .99975586
Test of hypothesis Ho: QualityTreatmentNeuN4==0.950828 :
>  p = .00097656

. signrank  AVotingCutOffNeutral4=44

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           1          39
    negative |       11          77          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffNeutral4 = 44
             z =  -2.981
    Prob > |z| =   0.0029

. permtest1  AVotingCutOffNeutral4=44
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffNeutral4-44
-------------------+---------------------------------
 observations      | 12
  - positive       | 1
  - negative       | 11
  - zero           | 0
-------------------+---------------------------------
  critical value   | -180.9875001907349


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffNeutral4>=44 : p = .
> 00048828
Test of hypothesis Ho: AVotingCutOffNeutral4<=44 : p = .
> 99975586
Test of hypothesis Ho: AVotingCutOffNeutral4==44 : p = .
> 00097656

. 
. /////////When Partisan Bias was Neutral and There were
>  5 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVNeutral5=mean(Willi
> ngness2Vote) if Neutral==1&HowManyHaveExpertise==5
(1155 missing values generated)

. by ElectorateID, sort: egen AvergesNeutral5=mean(MeanW
> TVNeutral5)
(207 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffNeutral5=Averg
> esNeutral5 if _n==1
(1,250 missing values generated)

. gen QualityTreatmentNeuN5=1-0.5*(1-AVotingCutOffNeutra
> l5/100)^5
(1,250 missing values generated)

. mean AVotingCutOffNeutral5

Mean estimation                   Number of obs   =     
>     10

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral5 |      28.63   3.575815      20.54
> 094                                                   
>        36.71906
--------------------------------------------------------
> ---------------

. mean QualityTreatmentNeuN5

Mean estimation                   Number of obs   =     
>     10

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentNeuN5 |    .887612   .0234631      .8345
> 348                                                   
>        .9406893
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentNeuN5=0.953074

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           4        27.5
    negative |        9          51        27.5
        zero |        0           0           0
-------------+---------------------------------
         all |       10          55          55

unadjusted variance       96.25
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         96.25

Ho: QualityTreatmentNeuN5 = 0.953074
             z =  -2.395
    Prob > |z| =   0.0166

. permtest1 QualityTreatmentNeuN5=0.953074
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentNeuN5-0.953074
-------------------+---------------------------------
 observations      | 10
  - positive       | 1
  - negative       | 9
  - zero           | 0
-------------------+---------------------------------
  critical value   | -.6546197307014461


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentNeuN5>=0.953074 :
>  p = .00878906
Test of hypothesis Ho: QualityTreatmentNeuN5<=0.953074 :
>  p = .9921875
Test of hypothesis Ho: QualityTreatmentNeuN5==0.953074 :
>  p = .01757813

. signrank  AVotingCutOffNeutral5=37.7

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           7        27.5
    negative |        9          48        27.5
        zero |        0           0           0
-------------+---------------------------------
         all |       10          55          55

unadjusted variance       96.25
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         96.25

Ho: AVotingCutOffNeutral5 = 37.7
             z =  -2.090
    Prob > |z| =   0.0367

. permtest1  AVotingCutOffNeutral5=37.7
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffNeutral5-37.7
-------------------+---------------------------------
 observations      | 10
  - positive       | 1
  - negative       | 9
  - zero           | 0
-------------------+---------------------------------
  critical value   | -90.69999885559085


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffNeutral5>=37.7 : p =
>  .01660156
Test of hypothesis Ho: AVotingCutOffNeutral5<=37.7 : p =
>  .984375
Test of hypothesis Ho: AVotingCutOffNeutral5==37.7 : p =
>  .03320313

. 
. 
. /////////When Partisan Bias was Supportive and There w
> as 1 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVSupportive1=mean(Wi
> llingness2Vote) if Supportive==1&HowManyHaveExpertise=
> =1
(1258 missing values generated)

. by ElectorateID, sort: egen AvergesSupportive1=mean(Me
> anWTVSupportive1)
(1158 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffSupportive1=Av
> ergesSupportive1 if _n==1
(1,259 missing values generated)

. gen QualityTreatmentSuppN1=1

. mean AVotingCutOffSupportive1

Mean estimation                   Number of obs   =     
>      1

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive1 |       37.5          .        
>      .                                                
>                  .
--------------------------------------------------------
> ------------------

. signrank AVotingCutOffSupportive1=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           1          .5
    negative |        0           0          .5
        zero |        0           0           0
-------------+---------------------------------
         all |        1           1           1

unadjusted variance        0.25
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance          0.25

Ho: AVotingCutOffSupportive1 = 0
             z =   1.000
    Prob > |z| =   0.3173

. permtest1 AVotingCutOffSupportive1=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffSupportive1-0
-------------------+---------------------------------
 observations      | 1
  - positive       | 1
  - negative       | 0
  - zero           | 0
-------------------+---------------------------------
  critical value   | 37.5


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffSupportive1>=0 : p =
>  1
Test of hypothesis Ho: AVotingCutOffSupportive1<=0 : p =
>  .5
Test of hypothesis Ho: AVotingCutOffSupportive1==0 : p =
>  1

. 
. 
. /////////When Partisan Bias was Supportive and There w
> ere 2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVSupportive2=mean(Wi
> llingness2Vote) if Supportive==1&HowManyHaveExpertise=
> =2
(1230 missing values generated)

. by ElectorateID, sort: egen AvergesSupportive2=mean(Me
> anWTVSupportive2)
(209 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffSupportive2=Av
> ergesSupportive2 if _n==1
(1,250 missing values generated)

. gen QualityTreatmentSuppN2=1

. mean AVotingCutOffSupportive2

Mean estimation                   Number of obs   =     
>     10

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive2 |       8.35   2.636601      2.
> 385593                                                
>           14.31441
--------------------------------------------------------
> ------------------

. signrank AVotingCutOffSupportive2=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        9          54          27
    negative |        0           0          27
        zero |        1           1           1
-------------+---------------------------------
         all |       10          55          55

unadjusted variance       96.25
adjustment for ties       -0.13
adjustment for zeros      -0.25
                     ----------
adjusted variance         95.88

Ho: AVotingCutOffSupportive2 = 0
             z =   2.757
    Prob > |z| =   0.0058

. permtest1 AVotingCutOffSupportive2=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffSupportive2-0
-------------------+---------------------------------
 observations      | 10
  - positive       | 9
  - negative       | 0
  - zero           | 1
-------------------+---------------------------------
  critical value   | 83.5


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffSupportive2>=0 : p =
>  1
Test of hypothesis Ho: AVotingCutOffSupportive2<=0 : p =
>  .00195313
Test of hypothesis Ho: AVotingCutOffSupportive2==0 : p =
>  .00390625

. 
. /////////When Partisan Bias was Supportive and There w
> ere 2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVSupportive3=mean(Wi
> llingness2Vote) if Supportive==1&HowManyHaveExpertise=
> =3
(1125 missing values generated)

. by ElectorateID, sort: egen AvergesSupportive3=mean(Me
> anWTVSupportive3)

. by ElectorateID, sort: gen AVotingCutOffSupportive3=Av
> ergesSupportive3 if _n==1
(1,248 missing values generated)

. gen QualityTreatmentSuppN3=1

. mean AVotingCutOffSupportive3

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive3 |   16.18843   2.983253       9
> .62233                                                
>           22.75452
--------------------------------------------------------
> ------------------

. signrank AVotingCutOffSupportive3=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |       12          78          39
    negative |        0           0          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffSupportive3 = 0
             z =   3.059
    Prob > |z| =   0.0022

. permtest1 AVotingCutOffSupportive3=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffSupportive3-0
-------------------+---------------------------------
 observations      | 12
  - positive       | 12
  - negative       | 0
  - zero           | 0
-------------------+---------------------------------
  critical value   | 194.2611126899719


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffSupportive3>=0 : p =
>  1
Test of hypothesis Ho: AVotingCutOffSupportive3<=0 : p =
>  .00024414
Test of hypothesis Ho: AVotingCutOffSupportive3==0 : p =
>  .00048828

. 
. /////////When Partisan Bias was Supportive and There w
> ere 2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVSupportive4=mean(Wi
> llingness2Vote) if Supportive==1&HowManyHaveExpertise=
> =4
(1120 missing values generated)

. by ElectorateID, sort: egen AvergesSupportive4=mean(Me
> anWTVSupportive4)

. by ElectorateID, sort: gen AVotingCutOffSupportive4=Av
> ergesSupportive4 if _n==1
(1,248 missing values generated)

. gen QualityTreatmentSuppN4=1

. mean AVotingCutOffSupportive4

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive4 |   11.72535   1.928021      7.
> 481802                                                
>           15.96889
--------------------------------------------------------
> ------------------

. signrank AVotingCutOffSupportive4=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |       12          78          39
    negative |        0           0          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffSupportive4 = 0
             z =   3.059
    Prob > |z| =   0.0022

. permtest1 AVotingCutOffSupportive4=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffSupportive4-0
-------------------+---------------------------------
 observations      | 12
  - positive       | 12
  - negative       | 0
  - zero           | 0
-------------------+---------------------------------
  critical value   | 140.7041683197021


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffSupportive4>=0 : p =
>  1
Test of hypothesis Ho: AVotingCutOffSupportive4<=0 : p =
>  .00024414
Test of hypothesis Ho: AVotingCutOffSupportive4==0 : p =
>  .00048828

. 
. /////////When Partisan Bias was Supportive and There w
> ere 2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVSupportive5=mean(Wi
> llingness2Vote) if Supportive==1&HowManyHaveExpertise=
> =5
(1155 missing values generated)

. by ElectorateID, sort: egen AvergesSupportive5=mean(Me
> anWTVSupportive5)
(103 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffSupportive5=Av
> ergesSupportive5 if _n==1
(1,249 missing values generated)

. gen QualityTreatmentSuppN5=1

. mean AVotingCutOffSupportive5

Mean estimation                   Number of obs   =     
>     11

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive5 |   13.09091   3.413748      5.
> 484604                                                
>           20.69721
--------------------------------------------------------
> ------------------

. signrank AVotingCutOffSupportive5=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |       11          66          33
    negative |        0           0          33
        zero |        0           0           0
-------------+---------------------------------
         all |       11          66          66

unadjusted variance      126.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        126.50

Ho: AVotingCutOffSupportive5 = 0
             z =   2.934
    Prob > |z| =   0.0033

. permtest1 AVotingCutOffSupportive5=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffSupportive5-0
-------------------+---------------------------------
 observations      | 11
  - positive       | 11
  - negative       | 0
  - zero           | 0
-------------------+---------------------------------
  critical value   | 143.9999990463257


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffSupportive5>=0 : p =
>  1
Test of hypothesis Ho: AVotingCutOffSupportive5<=0 : p =
>  .00048828
Test of hypothesis Ho: AVotingCutOffSupportive5==0 : p =
>  .00097656

. 
. restore

. 
. 
. 
. 
. 
. 
. //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> /////////                Online Appendix H            
>         ////////
> //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> preserve

. clear

. import excel "D:\FiguresReplications.xlsx",  sheet("Fi
> gureA234") firstrow

. //////////////////////////////////////////////////////
> ////////////////
> /////////                     Figure A2               
>         ////////
> //////////////////////////////////////////////////////
> ////////////////
> tw (line c mu if Partisan=="Against"&Group=="Control",
>  lcolor(gs10) lpattern(dash))||(line c mu if Partisan=
> ="Neutral"&Group=="Control",lcolor(gs10) lwidth(thick)
> )||(line c mu if Partisan=="Supportive"&Group=="Contro
> l",lcolor(black)), ylabel(0 (0.1) 0.6,nogrid) ytitle("
> Logit-QRE" "cutoff willingness to vote") xtitle("{&mu}
>  (noise parameter)") graphregion(color(white)) plotreg
> ion(color(white)) bgcolor(white) legend(region(lcolor(
> white)) order (1 2 3) symxsize(Medium) keygap(tiny) la
> bel (1 "Against") label( 2 "Neutral") label ( 3 "Suppo
> rtive") row(3) position (5) ring(0))
(note:  named style Medium not found in class gsize,
    default attributes used)

. graph export "D:\FigureA2.pdf", as(pdf) replace
(file D:\FigureA2.pdf written in PDF format)

. //////////////////////////////////////////////////////
> ////////////////
> /////////                     Figure A3               
>         ////////
> //////////////////////////////////////////////////////
> ////////////////
> tw (line c mu if Partisan=="Against"&Group=="Treatment
> ", lcolor(gs10) lpattern(dash))||(line c mu if Partisa
> n=="Neutral"&Group=="Treatment",lcolor(gs10) lwidth(th
> ick))||(line c mu if Partisan=="Supportive"&Group=="Tr
> eatment",lcolor(black)), ylabel(0 (0.1) 0.4,nogrid) yt
> itle("Logit-QRE" "cutoff willingness to vote") xtitle(
> "{&mu} (noise parameter)") graphregion(color(white)) p
> lotregion(color(white)) bgcolor(white) legend(region(l
> color(white)) order (1 2 3) symxsize(Medium) keygap(ti
> ny) label (1 "Against") label( 2 "Neutral") label ( 3 
> "Supportive") row(3) position (5) ring(0))
(note:  named style Medium not found in class gsize,
    default attributes used)

. graph export "D:\FigureA3.pdf", as(pdf) replace
(file D:\FigureA3.pdf written in PDF format)

. //////////////////////////////////////////////////////
> ////////////////
> /////////                     Figure A4               
>         ////////
> //////////////////////////////////////////////////////
> ////////////////
> tw (line c mu if Partisan=="Against"&Group=="Control",
>  name(Against,replace) lcolor(gs10) lpattern(dash) xax
> is(1 2) yaxis(1 2))||(line c mu if Partisan=="Against"
> &Group=="Treatment", lcolor(blue) lpattern(dash) lwidt
> h(thick)), ylabel(0 (0.1) 0.6,nogrid axis(1)) ylabel("
> ",nogrid axis(2)) xlabel("",nogrid axis(2)) ytitle("Lo
> git-QRE" "cutoff willingness to vote") xtitle("{&mu} (
> noise parameter)") xtitle("",axis(2)) ytitle("",axis(2
> )) graphregion(color(white)) plotregion(color(white)) 
> bgcolor(white) title("Against",color(black)) legend(re
> gion(lcolor(white)) order (1 2) symxsize(5) keygap(tin
> y) label (1 "Control") label( 2 "Treatment") row(2) po
> sition (5) ring(0))

. tw (line c mu if Partisan=="Neutral"&Group=="Control",
>  name(Neutral,replace) lcolor(gs10) lpattern(dash) xax
> is(1 2) yaxis(1 2))||(line c mu if Partisan=="Neutral"
> &Group=="Treatment", lcolor(blue) lpattern(dash) lwidt
> h(thick)), ylabel(0 (0.1) 0.6,nogrid axis(1)) ylabel("
> ",nogrid axis(2)) xlabel("",nogrid axis(2)) ytitle("")
>  xtitle("{&mu} (noise parameter)") xtitle("",axis(2)) 
> ytitle("",axis(2)) graphregion(color(white)) plotregio
> n(color(white)) bgcolor(white) title("Neutral",color(b
> lack)) legend(region(lcolor(white)) order (1 2) symxsi
> ze(5) keygap(tiny) label (1 "Control") label( 2 "Treat
> ment") row(2) position (5) ring(0))

. tw (line c mu if Partisan=="Supportive"&Group=="Contro
> l", name(Supportive,replace) lcolor(gs10) lpattern(das
> h) xaxis(1 2) yaxis(1 2))||(line c mu if Partisan=="Su
> pportive"&Group=="Treatment", lcolor(blue) lpattern(da
> sh) lwidth(thick)), ylabel(0 (0.1) 0.6,nogrid axis(1))
>  ylabel("",nogrid axis(2)) xlabel("",nogrid axis(2)) y
> title("") xtitle("{&mu} (noise parameter)") xtitle("",
> axis(2)) ytitle("",axis(2)) graphregion(color(white)) 
> plotregion(color(white)) bgcolor(white) title("Support
> ive",color(black)) legend(region(lcolor(white)) order 
> (1 2) symxsize(5) keygap(tiny) label (1 "Control") lab
> el( 2 "Treatment") row(2) position (5) ring(0))

. graph combine Against Neutral Supportive, name(FigureA
> 4,replace) row(1) graphregion(color(white)) plotregion
> (color(white))

. graph display FigureA4, xsize(12) ysize(6)

. graph export "D:\FigureA4.pdf", as(pdf) replace
(file D:\FigureA4.pdf written in PDF format)

. restore

. //////////////////////////////////////////////////////
> ////////////////
> /////////                     Table A5                
>         ////////
> //////////////////////////////////////////////////////
> ////////////////
> //In Table A5, we report the theoretical analysis of Q
> uantal Response Equilibrium//
. //For the Control Group//
. //The calculations used the symmetric Bayesian Nash eq
> uilibirum willingness to 
. //vote equations defined in line 20 on page 16 of Onli
> ne Appendix, and plug in that equiation to 
. //to the equation detailed in lines 17-20 on page 22 o
> f Online Appendix to 
. //calculate the willingness to vote of Control Group w
> hen partisan bias is against//
. //The calculations used the symmetric Bayesian Nash eq
> uilibirum willingness to 
. //vote equations defined in line 2 on page 17 of Onlin
> e Appendix, and plug in that equiation to 
. //to the equation detailed in lines 17-20 on page 22 o
> f Online Appendix to 
. //calculate the willingness to vote of Control Group w
> hen partisan bias is neutral//
. //We manually set WTV=0, which is derived from the ana
> lysis in lines 3-5 on page 17 of Online Appendix, 
. //and plug it to the equation detailed in lines 17-20 
> on page 22 of Online Appendix to 
. //calculate the willingness to vote of Control Group w
> hen partisan bias is supportive//
. //We manually averaged the point predictions of Agains
> t, Neutral, and Supportive and got the average willing
> ness to vote in Control Group is 39.2
. 
. //For the Treatment Group//
. //The calculations used the symmetric Bayesian Nash eq
> uilibirum willingness to 
. //vote equations defined in lines 6-7 on page 18 of On
> line Appendix, and plug in that equiation to 
. //to the equation detailed in lines 17-20 on page 22 o
> f Online Appendix to 
. //calculate the willingness to vote of Treatment Group
> //
. //As noted in line 9 on page 20 of Online Appendix, in
>  the calculations of point predictions, we set d=s=0
. //We manually averaged the point predictions of Agains
> t, Neutral, and Supportive and got the average willing
> ness to vote in Treatment Group is 26.6.
. 
. 
. //The experimental results mentioned in the table are 
> based on the statistics derived by this do file, copie
> d from Lines 108-161
. *When partisan bias is against
. mean Willingness2Vote if Treatment=="ControlGroup"&Exp
> ertise==1&Against==1

Mean estimation                   Number of obs   =     
>    463

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |     51.527   1.630356      48.32316  
>   54.73083
--------------------------------------------------------
> ----------

. mean Willingness2Vote if Treatment=="TreatmentGroup"&E
> xpertise==1&Against==1

Mean estimation                   Number of obs   =     
>    422

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   32.35071   1.320294      29.75552  
>    34.9459
--------------------------------------------------------
> ----------

. preserve

. drop if Expertise==0
(1,089 observations deleted)

. drop if Against!=1
(1,626 observations deleted)

. mean Willingness2Vote if Treatment=="ControlGroup"

Mean estimation                   Number of obs   =     
>    463

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |     51.527   1.630356      48.32316  
>   54.73083
--------------------------------------------------------
> ----------

. mean Willingness2Vote if Treatment=="TreatmentGroup"

Mean estimation                   Number of obs   =     
>    422

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   32.35071   1.320294      29.75552  
>    34.9459
--------------------------------------------------------
> ----------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTV=mean(Willingnes
> s2Vote)

. by GlobalSubjectID, sort: gen AVotingCutOff=MeanWTV if
>  _n==1
(765 missing values generated)

. 
. ranksum AVotingCutOff,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
ControlGroup |       60        4465        3630
TreatmentGro |       60        2795        3630
-------------+---------------------------------
    combined |      120        7260        7260

unadjusted variance    36300.00
adjustment for ties       -2.65
                     ----------
adjusted variance      36297.35

Ho: AVotin~f(Treatm~t==ControlGroup) = AVotin~f(Treatm~t
> ==TreatmentGroup)
             z =   4.383
    Prob > |z| =   0.0000

. permtest2 AVotingCutOff,by(FPTestIndicator)
Fisher-Pitman permutation test for two independent sampl
> es


FPTestIndi~r |      obs        mean    std.dev.
-------------+---------------------------------
           0 |       60   51.845493   23.957607
           1 |       60   33.166317   19.388478
-------------+---------------------------------
    combined |      120   42.505905   23.641274


mode of operation:  Montecarlo simulation (200000 runs)

Progress:  |........................................|

Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  >= AVotingCutOff(FPTestIndicator==1) :  p=1 (one-tail
> ed)
Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  <= AVotingCutOff(FPTestIndicator==1) :  p=0 (one-tail
> ed)
Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  == AVotingCutOff(FPTestIndicator==1) :  p=0 (two-tail
> ed)

. restore

. 
. 
. 
. *When partisan bias is neutral
. mean Willingness2Vote if Treatment=="ControlGroup"&Exp
> ertise==1&Neutral==1

Mean estimation                   Number of obs   =     
>    392

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |    46.3699   1.483668      43.45293  
>   49.28686
--------------------------------------------------------
> ----------

. mean Willingness2Vote if Treatment=="TreatmentGroup"&E
> xpertise==1&Neutral==1

Mean estimation                   Number of obs   =     
>    426

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   28.45305    1.11643      26.25864  
>   30.64746
--------------------------------------------------------
> ----------

. preserve

. drop if Expertise==0
(1,089 observations deleted)

. drop if Neutral!=1
(1,693 observations deleted)

. mean Willingness2Vote if Treatment=="ControlGroup"

Mean estimation                   Number of obs   =     
>    392

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |    46.3699   1.483668      43.45293  
>   49.28686
--------------------------------------------------------
> ----------

. mean Willingness2Vote if Treatment=="TreatmentGroup"

Mean estimation                   Number of obs   =     
>    426

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   28.45305    1.11643      26.25864  
>   30.64746
--------------------------------------------------------
> ----------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTV=mean(Willingnes
> s2Vote)

. by GlobalSubjectID, sort: gen AVotingCutOff=MeanWTV if
>  _n==1
(698 missing values generated)

. 
. ranksum AVotingCutOff,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
ControlGroup |       60        4485        3630
TreatmentGro |       60        2775        3630
-------------+---------------------------------
    combined |      120        7260        7260

unadjusted variance    36300.00
adjustment for ties       -3.66
                     ----------
adjusted variance      36296.34

Ho: AVotin~f(Treatm~t==ControlGroup) = AVotin~f(Treatm~t
> ==TreatmentGroup)
             z =   4.488
    Prob > |z| =   0.0000

. permtest2 AVotingCutOff,by(FPTestIndicator)
Fisher-Pitman permutation test for two independent sampl
> es


FPTestIndi~r |      obs        mean    std.dev.
-------------+---------------------------------
           0 |       60   47.429768    25.83547
           1 |       60   28.191164   15.068936
-------------+---------------------------------
    combined |      120   37.810466   23.169422


mode of operation:  Montecarlo simulation (200000 runs)

Progress:  |........................................|

Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  >= AVotingCutOff(FPTestIndicator==1) :  p=1 (one-tail
> ed)
Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  <= AVotingCutOff(FPTestIndicator==1) :  p=0 (one-tail
> ed)
Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  == AVotingCutOff(FPTestIndicator==1) :  p=0 (two-tail
> ed)

. restore

. 
. 
. 
. *When partisan bias is supportive
. mean Willingness2Vote if Treatment=="ControlGroup"&Exp
> ertise==1&Supportive==1

Mean estimation                   Number of obs   =     
>    396

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   21.28788   1.436463      18.46381  
>   24.11195
--------------------------------------------------------
> ----------

. mean Willingness2Vote if Treatment=="TreatmentGroup"&E
> xpertise==1&Supportive==1

Mean estimation                   Number of obs   =     
>    412

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   13.64806   1.067955      11.54872  
>   15.74739
--------------------------------------------------------
> ----------

. preserve

. drop if Expertise==0
(1,089 observations deleted)

. drop if Supportive!=1
(1,703 observations deleted)

. mean Willingness2Vote if Treatment=="ControlGroup"

Mean estimation                   Number of obs   =     
>    396

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   21.28788   1.436463      18.46381  
>   24.11195
--------------------------------------------------------
> ----------

. mean Willingness2Vote if Treatment=="TreatmentGroup"

Mean estimation                   Number of obs   =     
>    412

--------------------------------------------------------
> ----------
                 |       Mean   Std. Err.     [95% Conf.
>  Interval]
-----------------+--------------------------------------
> ----------
Willingness2Vote |   13.64806   1.067955      11.54872  
>   15.74739
--------------------------------------------------------
> ----------

. 
. sort GlobalSubjectID

. by GlobalSubjectID, sort: egen MeanWTV=mean(Willingnes
> s2Vote)

. by GlobalSubjectID, sort: gen AVotingCutOff=MeanWTV if
>  _n==1
(688 missing values generated)

. 
. ranksum AVotingCutOff,by(Treatment)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

   Treatment |      obs    rank sum    expected
-------------+---------------------------------
ControlGroup |       60      3946.5        3630
TreatmentGro |       60      3313.5        3630
-------------+---------------------------------
    combined |      120        7260        7260

unadjusted variance    36300.00
adjustment for ties     -257.02
                     ----------
adjusted variance      36042.98

Ho: AVotin~f(Treatm~t==ControlGroup) = AVotin~f(Treatm~t
> ==TreatmentGroup)
             z =   1.667
    Prob > |z| =   0.0955

. permtest2 AVotingCutOff,by(FPTestIndicator)
Fisher-Pitman permutation test for two independent sampl
> es


FPTestIndi~r |      obs        mean    std.dev.
-------------+---------------------------------
           0 |       60   21.913669   22.798907
           1 |       60   13.893737   15.785456
-------------+---------------------------------
    combined |      120   17.903703   19.936634


mode of operation:  Montecarlo simulation (200000 runs)

Progress:  |........................................|

Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  >= AVotingCutOff(FPTestIndicator==1) :  p=.98743 (one
> -tailed)
Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  <= AVotingCutOff(FPTestIndicator==1) :  p=.01257 (one
> -tailed)
Test of hypothesis Ho: AVotingCutOff(FPTestIndicator==0)
>  == AVotingCutOff(FPTestIndicator==1) :  p=.02514 (two
> -tailed)

. restore

. 
. //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> /////////                Online Appendix I            
>         ////////
> //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> /////////                     Table A6                
>         ////////
> //////////////////////////////////////////////////////
> ////////////////
> //////////////////////////////////////////////////////
> ////////////////
> //In Table A6, we report the theoretical analysis of U
> tilitarian Welfare//
. //The utilitarian planner's symmetric cost vote cutoff
>  prescription are calculated and detailed in Online Ap
> pendix I//
. //Specifically, in line 8 on page 29 of Online Appendi
> x, 
. //we report point predictions of willingness to vote w
> hen partisan bias is Supportive in Control Group
. //In lines 9-19 on page 29 of Online Appendix, 
. //we report how we manually calculate point prediction
> s of willingness to vote when partisan bias is Neutral
>  in Control Group
. //In line 20 on page 29 and lines 1-5 on page 30 of On
> line Appendix, 
. //we report how we manually calculate point prediction
> s of willingness to vote when partisan bias is Against
>  in Control Group.
. //In line 5 on page 26 of Online Appendix, 
. //we report how we manually calculate point prediction
> s of willingness to vote when partisan bias is Support
> ive in Treatment Group
. //In lines 6-19 on page 26 and lines 1-14 on page 27 o
> f Online Appendix, 
. //we report how we manually calculate point prediction
> s of willingness to vote when partisan bias is Neutral
>  in Treatment Group
. //In lines 20-26 on page 27 and lines 1-16 on page 28 
> and lines 1-4 on page 29 of Online Appendix, 
. //we report how we manually calculate point prediction
> s of willingness to vote when partisan bias is Against
>  in Treatment Group
. 
. 
. 
. //////////////////////////////////////////////////////
> ////////////////
> /////////                      Table A7               
>         ////////
> //////////////////////////////////////////////////////
> ////////////////
> //In our experiment, the number of expert voters was e
> xogenously, randomly, and independently determined by 
> the computer.  
. //Recall that in the Treatment Group, subjects were to
> ld the realized number of expert voters. 
. //While on average 70% of voters are expert voters, in
>  specific voting round, the number of expert voters co
> uld be 1, 2, 3, 4, or 5. 
. //Hence, the realized number of expert voters is denot
> ed as M=1, M=2, M=3, M=4, and M=5 in the Online Append
> ix I and in Table A7. 
. //However, in the Control Group, subjects were not tol
> d the realized number of expert voters. We thus only r
> eport the average effects in the column of Control Gro
> up.
. //We use both Mann-Whiney sign-rank test and the exact
>  Fisher-Pitman permutation test 
. //to examine whether the experimental observations are
>  different from the utilitarian 
. //planners' prescription. The numbers reported in Tabl
> e A7 are p-values of statistical tests. 
. //For the Treatment Group, the p-values are reported b
> y the number of exogenously realized 
. //expert voters and the type of statistical tests. For
>  the Control Group, 
. //the p-values are reported by the type of statistical
>  tests.
. 
. //We use the electorate averages as the unit of indepe
> ndent observation in the statistical analysis. 
. //We have a total of 12 electorates in the Control Gro
> up and 12 electorates in the Treatment Group. 
. //In the Control Group, since we pooled the average ef
> fects together in the analysis, the number of observat
> ions is 12. 
. //In the Treatment Group, since we break down the anal
> ysis by the realized number of expert voters, 
. //the number of observations is reported by the realiz
> ation of parameters in our experiments. 
. //The setting of the experiment is that in an electora
> te of 5 voters about 70% of voters are expert voters, 
. //which explains there are more observations when M=3 
> and M=4 as compared to when M=1, M=2, and M=5.
. //We performed statistical tests of both voters' willi
> ngness to vote and the quality 
. //of democratic choice and report these results in Pan
> el A and Panel B of Table A7, respectively. 
. //The statistical results are reported by the level of
>  partisan bias in each panel.
. //In Table A7, the statistics are derived from the ana
> lysis of this do file codes, copied from Lines 595-834
> . 
. //Using Lines 617-628 as an illustrative example. 
. //The codes in these lines derive the statistical resu
> lts for M=2 when the partisan bias is against. 
. //At the electorate level, there are 8 observations. F
> or the comparison between 
. //observed willingness to vote and point predictions, 
> the p-value of the two-sided 
. //Mann-Whiney sign-rank is 0.0116, and the p-value of 
> the two-sided exact Fisher-Pitman permutation test is 
> 0.0078. 
. //These p-values are reported in Panel A, Against, M=2
> . For the comparisons between the observed quality of 
. //democratic choice and point predictions, the p-value
>  of the two-sided Mann-Whiney sign-rank is 0.0116, 
. //and the p-value of the two-sided exact Fisher-Pitman
>  permutation test is 0.0078. 
. //These p-values are reported in Panel B, Against, M=2
> . 
. 
. preserve

. *We first focus on the behavior of expert voters in th
> e Treatment Group
. drop if Expertise==0
(1,089 observations deleted)

. drop if Treatment=="ControlGroup"
(1,251 observations deleted)

. 
. 
. /////////When Partisan Bias was Against and There was 
> 1 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVAgainst1=mean(Willi
> ngness2Vote) if Against==1&HowManyHaveExpertise==1
(1256 missing values generated)

. by ElectorateID, sort: egen AvergesAgainst1=mean(MeanW
> TVAgainst1)
(933 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffAgainst1=Averg
> esAgainst1 if _n==1
(1,257 missing values generated)

. gen QualityTreatmentAgaN1=0

. mean AVotingCutOffAgainst1

Mean estimation                   Number of obs   =     
>      3

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst1 |   5.833333   4.639804     -14.13
> 013                                                   
>         25.7968
--------------------------------------------------------
> ---------------

. mean QualityTreatmentAgaN1

Mean estimation                   Number of obs   =     
>  1,260

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentAgaN1 |          0  (omitted)
--------------------------------------------------------
> ---------------

. signrank  AVotingCutOffAgainst1=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        2           5         2.5
    negative |        0           0         2.5
        zero |        1           1           1
-------------+---------------------------------
         all |        3           6           6

unadjusted variance        3.50
adjustment for ties        0.00
adjustment for zeros      -0.25
                     ----------
adjusted variance          3.25

Ho: AVotingCutOffAgainst1 = 0
             z =   1.387
    Prob > |z| =   0.1655

. permtest1  AVotingCutOffAgainst1=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffAgainst1-0
-------------------+---------------------------------
 observations      | 3
  - positive       | 2
  - negative       | 0
  - zero           | 1
-------------------+---------------------------------
  critical value   | 17.5


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffAgainst1>=0 : p = 1
Test of hypothesis Ho: AVotingCutOffAgainst1<=0 : p = .2
> 5
Test of hypothesis Ho: AVotingCutOffAgainst1==0 : p = .5

. 
. /////////When Partisan Bias was Against and There were
>  2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVAgainst2=mean(Willi
> ngness2Vote) if Against==1&HowManyHaveExpertise==2
(1234 missing values generated)

. by ElectorateID, sort: egen AvergesAgainst2=mean(MeanW
> TVAgainst2)
(432 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffAgainst2=Averg
> esAgainst2 if _n==1
(1,252 missing values generated)

. gen QualityTreatmentAgaN2=(AVotingCutOffAgainst2/100)^
> 2
(1,252 missing values generated)

. mean AVotingCutOffAgainst2

Mean estimation                   Number of obs   =     
>      8

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst2 |   27.26042   6.667995      11.49
> 311                                                   
>        43.02772
--------------------------------------------------------
> ---------------

. mean QualityTreatmentAgaN2

Mean estimation                   Number of obs   =     
>      8

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentAgaN2 |   .1054365   .0337554      .0256
> 176                                                   
>        .1852555
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentAgaN2=1

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          18
    negative |        8          36          18
        zero |        0           0           0
-------------+---------------------------------
         all |        8          36          36

unadjusted variance       51.00
adjustment for ties       -0.13
adjustment for zeros       0.00
                     ----------
adjusted variance         50.88

Ho: QualityTreatmentAgaN2 = 1
             z =  -2.524
    Prob > |z| =   0.0116

. permtest1 QualityTreatmentAgaN2=1
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentAgaN2-1
-------------------+---------------------------------
 observations      | 8
  - positive       | 0
  - negative       | 8
  - zero           | 0
-------------------+---------------------------------
  critical value   | -7.156507655819951


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentAgaN2>=1 : p = .0
> 0390625
Test of hypothesis Ho: QualityTreatmentAgaN2<=1 : p = 1
Test of hypothesis Ho: QualityTreatmentAgaN2==1 : p = .0
> 078125

. signrank  AVotingCutOffAgainst2=100

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          18
    negative |        8          36          18
        zero |        0           0           0
-------------+---------------------------------
         all |        8          36          36

unadjusted variance       51.00
adjustment for ties       -0.13
adjustment for zeros       0.00
                     ----------
adjusted variance         50.88

Ho: AVotingCutOffAgainst2 = 100
             z =  -2.524
    Prob > |z| =   0.0116

. permtest1  AVotingCutOffAgainst2=100
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffAgainst2-100
-------------------+---------------------------------
 observations      | 8
  - positive       | 0
  - negative       | 8
  - zero           | 0
-------------------+---------------------------------
  critical value   | -581.9166679382324


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffAgainst2>=100 : p = 
> .00390625
Test of hypothesis Ho: AVotingCutOffAgainst2<=100 : p = 
> 1
Test of hypothesis Ho: AVotingCutOffAgainst2==100 : p = 
> .0078125

. 
. /////////When Partisan Bias was Against and There were
>  3 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVAgainst3=mean(Willi
> ngness2Vote) if Against==1&HowManyHaveExpertise==3
(1140 missing values generated)

. by ElectorateID, sort: egen AvergesAgainst3=mean(MeanW
> TVAgainst3)
(112 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffAgainst3=Averg
> esAgainst3 if _n==1
(1,249 missing values generated)

. gen QualityTreatmentAgaN3=comb(3,3)*(AVotingCutOffAgai
> nst3/100)^3+0.5*comb(3,2)*((AVotingCutOffAgainst3/100)
> ^2)*(1-(AVotingCutOffAgainst3/100))
(1,249 missing values generated)

. mean AVotingCutOffAgainst3

Mean estimation                   Number of obs   =     
>     11

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst3 |   35.41306   3.641884      27.29
> 844                                                   
>        43.52768
--------------------------------------------------------
> ---------------

. mean QualityTreatmentAgaN3

Mean estimation                   Number of obs   =     
>     11

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentAgaN3 |   .1779707   .0354245        .09
> 904                                                   
>        .2569014
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentAgaN3=1

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          33
    negative |       11          66          33
        zero |        0           0           0
-------------+---------------------------------
         all |       11          66          66

unadjusted variance      126.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        126.50

Ho: QualityTreatmentAgaN3 = 1
             z =  -2.934
    Prob > |z| =   0.0033

. permtest1 QualityTreatmentAgaN3=1
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentAgaN3-1
-------------------+---------------------------------
 observations      | 11
  - positive       | 0
  - negative       | 11
  - zero           | 0
-------------------+---------------------------------
  critical value   | -9.042322549968958


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentAgaN3>=1 : p = .0
> 0048828
Test of hypothesis Ho: QualityTreatmentAgaN3<=1 : p = 1
Test of hypothesis Ho: QualityTreatmentAgaN3==1 : p = .0
> 0097656

. signrank  AVotingCutOffAgainst3=100

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          33
    negative |       11          66          33
        zero |        0           0           0
-------------+---------------------------------
         all |       11          66          66

unadjusted variance      126.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        126.50

Ho: AVotingCutOffAgainst3 = 100
             z =  -2.934
    Prob > |z| =   0.0033

. permtest1  AVotingCutOffAgainst3=100
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffAgainst3-100
-------------------+---------------------------------
 observations      | 11
  - positive       | 0
  - negative       | 11
  - zero           | 0
-------------------+---------------------------------
  critical value   | -710.4563522338867


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffAgainst3>=100 : p = 
> .00048828
Test of hypothesis Ho: AVotingCutOffAgainst3<=100 : p = 
> 1
Test of hypothesis Ho: AVotingCutOffAgainst3==100 : p = 
> .00097656

. 
. /////////When Partisan Bias was Against and There were
>  4 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVAgainst4=mean(Willi
> ngness2Vote) if Against==1&HowManyHaveExpertise==4
(1048 missing values generated)

. by ElectorateID, sort: egen AvergesAgainst4=mean(MeanW
> TVAgainst4)

. by ElectorateID, sort: gen AVotingCutOffAgainst4=Averg
> esAgainst4 if _n==1
(1,248 missing values generated)

. gen QualityTreatmentAgaN4=comb(4,3)*((AVotingCutOffAga
> inst4/100)^3)*(1-(AVotingCutOffAgainst4/100))+0.5*comb
> (4,2)*((AVotingCutOffAgainst4/100)^2)*(1-(AVotingCutOf
> fAgainst3/100)^2)
(1,249 missing values generated)

. mean AVotingCutOffAgainst4

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst4 |   34.32882   3.422976       26.7
> 949                                                   
>        41.86274
--------------------------------------------------------
> ---------------

. mean QualityTreatmentAgaN4

Mean estimation                   Number of obs   =     
>     11

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentAgaN4 |   .4638175   .1015254      .2376
> 048                                                   
>        .6900302
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentAgaN4=0.951638

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           2          33
    negative |       10          64          33
        zero |        0           0           0
-------------+---------------------------------
         all |       11          66          66

unadjusted variance      126.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        126.50

Ho: QualityTreatmentAgaN4 = 0.951638
             z =  -2.756
    Prob > |z| =   0.0058

. permtest1 QualityTreatmentAgaN4=0.951638
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentAgaN4-0.951638
-------------------+---------------------------------
 observations      | 11
  - positive       | 1
  - negative       | 10
  - zero           | 0
-------------------+---------------------------------
  critical value   | -5.366025221519946


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentAgaN4>=0.951638 :
>  p = .00146484
Test of hypothesis Ho: QualityTreatmentAgaN4<=0.951638 :
>  p = .99902344
Test of hypothesis Ho: QualityTreatmentAgaN4==0.951638 :
>  p = .00292969

. signrank  AVotingCutOffAgainst4=86.7

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          39
    negative |       12          78          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffAgainst4 = 86.7
             z =  -3.059
    Prob > |z| =   0.0022

. permtest1  AVotingCutOffAgainst4=86.7
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffAgainst4-86.7
-------------------+---------------------------------
 observations      | 12
  - positive       | 0
  - negative       | 12
  - zero           | 0
-------------------+---------------------------------
  critical value   | -628.4541667938233


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffAgainst4>=86.7 : p =
>  .00024414
Test of hypothesis Ho: AVotingCutOffAgainst4<=86.7 : p =
>  1
Test of hypothesis Ho: AVotingCutOffAgainst4==86.7 : p =
>  .00048828

. 
. /////////When Partisan Bias was Against and There were
>  5 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVAgainst5=mean(Willi
> ngness2Vote) if Against==1&HowManyHaveExpertise==5
(1200 missing values generated)

. by ElectorateID, sort: egen AvergesAgainst5=mean(MeanW
> TVAgainst5)
(416 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffAgainst5=Averg
> esAgainst5 if _n==1
(1,252 missing values generated)

. gen QualityTreatmentAgaN5=comb(5,3)*((AVotingCutOffAga
> inst5/100)^3)*(1-(AVotingCutOffAgainst4/100))^2+0.5*co
> mb(5,2)*((AVotingCutOffAgainst5/100)^2)*(1-(AVotingCut
> OffAgainst3/100)^5)
(1,253 missing values generated)

. mean AVotingCutOffAgainst5

Mean estimation                   Number of obs   =     
>      8

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffAgainst5 |    29.6875   4.147264      19.88
> 078                                                   
>        39.49422
--------------------------------------------------------
> ---------------

. mean QualityTreatmentAgaN5

Mean estimation                   Number of obs   =     
>      7

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentAgaN5 |   .6443061   .1963658      .1638
> 163                                                   
>        1.124796
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentAgaN5=0.880517

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        2           8          14
    negative |        5          20          14
        zero |        0           0           0
-------------+---------------------------------
         all |        7          28          28

unadjusted variance       35.00
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         35.00

Ho: QualityTreatmentAgaN5 = 0.880517
             z =  -1.014
    Prob > |z| =   0.3105

. permtest1 QualityTreatmentAgaN5=0.880517
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentAgaN5-0.880517
-------------------+---------------------------------
 observations      | 7
  - positive       | 2
  - negative       | 5
  - zero           | 0
-------------------+---------------------------------
  critical value   | -1.653476122302055


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentAgaN5>=0.880517 :
>  p = .15625
Test of hypothesis Ho: QualityTreatmentAgaN5<=0.880517 :
>  p = .8515625
Test of hypothesis Ho: QualityTreatmentAgaN5==0.880517 :
>  p = .3125

. signrank  AVotingCutOffAgainst5=67.5

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          18
    negative |        8          36          18
        zero |        0           0           0
-------------+---------------------------------
         all |        8          36          36

unadjusted variance       51.00
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         51.00

Ho: AVotingCutOffAgainst5 = 67.5
             z =  -2.521
    Prob > |z| =   0.0117

. permtest1  AVotingCutOffAgainst5=67.5
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffAgainst5-67.5
-------------------+---------------------------------
 observations      | 8
  - positive       | 0
  - negative       | 8
  - zero           | 0
-------------------+---------------------------------
  critical value   | -302.5


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffAgainst5>=67.5 : p =
>  .00390625
Test of hypothesis Ho: AVotingCutOffAgainst5<=67.5 : p =
>  1
Test of hypothesis Ho: AVotingCutOffAgainst5==67.5 : p =
>  .0078125

. 
. 
. /////////When Partisan Bias was Neutral and There was 
> 1 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVNeutral1=mean(Willi
> ngness2Vote) if Neutral==1&HowManyHaveExpertise==1
(1257 missing values generated)

. by ElectorateID, sort: egen AvergesNeutral1=mean(MeanW
> TVNeutral1)
(961 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffNeutral1=Averg
> esNeutral1 if _n==1
(1,257 missing values generated)

. gen QualityTreatmentNeuN1=1-0.5*(1-AVotingCutOffNeutra
> l1/100)
(1,257 missing values generated)

. mean AVotingCutOffNeutral1

Mean estimation                   Number of obs   =     
>      3

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral1 |   23.33333   14.52966     -39.18
> 276                                                   
>        85.84943
--------------------------------------------------------
> ---------------

. mean QualityTreatmentNeuN1

Mean estimation                   Number of obs   =     
>      3

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentNeuN1 |   .6166667   .0726483      .3040
> 862                                                   
>        .9292471
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentNeuN1=1

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0           3
    negative |        3           6           3
        zero |        0           0           0
-------------+---------------------------------
         all |        3           6           6

unadjusted variance        3.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance          3.50

Ho: QualityTreatmentNeuN1 = 1
             z =  -1.604
    Prob > |z| =   0.1088

. permtest1 QualityTreatmentNeuN1=1
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentNeuN1-1
-------------------+---------------------------------
 observations      | 3
  - positive       | 0
  - negative       | 3
  - zero           | 0
-------------------+---------------------------------
  critical value   | -1.149999976158142


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentNeuN1>=1 : p = .1
> 25
Test of hypothesis Ho: QualityTreatmentNeuN1<=1 : p = 1
Test of hypothesis Ho: QualityTreatmentNeuN1==1 : p = .2
> 5

. signrank  AVotingCutOffNeutral1=100

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0           3
    negative |        3           6           3
        zero |        0           0           0
-------------+---------------------------------
         all |        3           6           6

unadjusted variance        3.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance          3.50

Ho: AVotingCutOffNeutral1 = 100
             z =  -1.604
    Prob > |z| =   0.1088

. permtest1  AVotingCutOffNeutral1=100
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffNeutral1-100
-------------------+---------------------------------
 observations      | 3
  - positive       | 0
  - negative       | 3
  - zero           | 0
-------------------+---------------------------------
  critical value   | -230


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffNeutral1>=100 : p = 
> .125
Test of hypothesis Ho: AVotingCutOffNeutral1<=100 : p = 
> 1
Test of hypothesis Ho: AVotingCutOffNeutral1==100 : p = 
> .25

. 
. /////////When Partisan Bias was Neutral and There were
>  2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVNeutral2=mean(Willi
> ngness2Vote) if Neutral==1&HowManyHaveExpertise==2
(1232 missing values generated)

. by ElectorateID, sort: egen AvergesNeutral2=mean(MeanW
> TVNeutral2)
(325 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffNeutral2=Averg
> esNeutral2 if _n==1
(1,251 missing values generated)

. gen QualityTreatmentNeuN2=1-0.5*(1-AVotingCutOffNeutra
> l2/100)^2
(1,251 missing values generated)

. mean AVotingCutOffNeutral2

Mean estimation                   Number of obs   =     
>      9

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral2 |   31.16667   5.608928      18.23
> 246                                                   
>        44.10088
--------------------------------------------------------
> ---------------

. mean QualityTreatmentNeuN2

Mean estimation                   Number of obs   =     
>      9

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentNeuN2 |   .7505146   .0354732      .6687
> 133                                                   
>        .8323159
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentNeuN2=0.959184

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0        22.5
    negative |        9          45        22.5
        zero |        0           0           0
-------------+---------------------------------
         all |        9          45          45

unadjusted variance       71.25
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         71.25

Ho: QualityTreatmentNeuN2 = 0.959184
             z =  -2.666
    Prob > |z| =   0.0077

. permtest1 QualityTreatmentNeuN2=0.959184
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentNeuN2-0.959184
-------------------+---------------------------------
 observations      | 9
  - positive       | 0
  - negative       | 9
  - zero           | 0
-------------------+---------------------------------
  critical value   | -1.878024778705598


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentNeuN2>=0.959184 :
>  p = .00195313
Test of hypothesis Ho: QualityTreatmentNeuN2<=0.959184 :
>  p = 1
Test of hypothesis Ho: QualityTreatmentNeuN2==0.959184 :
>  p = .00390625

. signrank  AVotingCutOffNeutral2=71.4

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0        22.5
    negative |        9          45        22.5
        zero |        0           0           0
-------------+---------------------------------
         all |        9          45          45

unadjusted variance       71.25
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         71.25

Ho: AVotingCutOffNeutral2 = 71.4
             z =  -2.666
    Prob > |z| =   0.0077

. permtest1  AVotingCutOffNeutral2=71.4
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffNeutral2-71.4
-------------------+---------------------------------
 observations      | 9
  - positive       | 0
  - negative       | 9
  - zero           | 0
-------------------+---------------------------------
  critical value   | -362.1


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffNeutral2>=71.4 : p =
>  .00195313
Test of hypothesis Ho: AVotingCutOffNeutral2<=71.4 : p =
>  1
Test of hypothesis Ho: AVotingCutOffNeutral2==71.4 : p =
>  .00390625

. 
. /////////When Partisan Bias was Neutral and There were
>  3 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVNeutral3=mean(Willi
> ngness2Vote) if Neutral==1&HowManyHaveExpertise==3
(1146 missing values generated)

. by ElectorateID, sort: egen AvergesNeutral3=mean(MeanW
> TVNeutral3)

. by ElectorateID, sort: gen AVotingCutOffNeutral3=Averg
> esNeutral3 if _n==1
(1,248 missing values generated)

. gen QualityTreatmentNeuN3=1-0.5*(1-AVotingCutOffNeutra
> l3/100)^3
(1,248 missing values generated)

. mean AVotingCutOffNeutral3

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral3 |   29.35231   2.229159      24.44
> 597                                                   
>        34.25866
--------------------------------------------------------
> ---------------

. mean QualityTreatmentNeuN3

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentNeuN3 |   .8179367   .0167815      .7810
> 009                                                   
>        .8548725
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentNeuN3=0.950269

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          39
    negative |       12          78          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties       -0.13
adjustment for zeros       0.00
                     ----------
adjusted variance        162.38

Ho: QualityTreatmentNeuN3 = 0.950269
             z =  -3.061
    Prob > |z| =   0.0022

. permtest1 QualityTreatmentNeuN3=0.950269
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentNeuN3-0.950269
-------------------+---------------------------------
 observations      | 12
  - positive       | 0
  - negative       | 12
  - zero           | 0
-------------------+---------------------------------
  critical value   | -1.587987676456452


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentNeuN3>=0.950269 :
>  p = .00024414
Test of hypothesis Ho: QualityTreatmentNeuN3<=0.950269 :
>  p = 1
Test of hypothesis Ho: QualityTreatmentNeuN3==0.950269 :
>  p = .00048828

. signrank  AVotingCutOffNeutral3=53.7

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          39
    negative |       12          78          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties       -0.13
adjustment for zeros       0.00
                     ----------
adjusted variance        162.38

Ho: AVotingCutOffNeutral3 = 53.7
             z =  -3.061
    Prob > |z| =   0.0022

. permtest1  AVotingCutOffNeutral3=53.7
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffNeutral3-53.7
-------------------+---------------------------------
 observations      | 12
  - positive       | 0
  - negative       | 12
  - zero           | 0
-------------------+---------------------------------
  critical value   | -292.1722206115723


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffNeutral3>=53.7 : p =
>  .00024414
Test of hypothesis Ho: AVotingCutOffNeutral3<=53.7 : p =
>  1
Test of hypothesis Ho: AVotingCutOffNeutral3==53.7 : p =
>  .00048828

. 
. /////////When Partisan Bias was Neutral and There were
>  4 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVNeutral4=mean(Willi
> ngness2Vote) if Neutral==1&HowManyHaveExpertise==4
(1084 missing values generated)

. by ElectorateID, sort: egen AvergesNeutral4=mean(MeanW
> TVNeutral4)

. by ElectorateID, sort: gen AVotingCutOffNeutral4=Averg
> esNeutral4 if _n==1
(1,248 missing values generated)

. gen QualityTreatmentNeuN4=1-0.5*(1-AVotingCutOffNeutra
> l4/100)^4
(1,248 missing values generated)

. mean AVotingCutOffNeutral4

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral4 |   28.91771   2.884807      22.56
> 829                                                   
>        35.26713
--------------------------------------------------------
> ---------------

. mean QualityTreatmentNeuN4

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentNeuN4 |   .8585247   .0214247      .8113
> 691                                                   
>        .9056802
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentNeuN4=0.950828

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           1          39
    negative |       11          77          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: QualityTreatmentNeuN4 = 0.950828
             z =  -2.981
    Prob > |z| =   0.0029

. permtest1 QualityTreatmentNeuN4=0.950828
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentNeuN4-0.950828
-------------------+---------------------------------
 observations      | 12
  - positive       | 1
  - negative       | 11
  - zero           | 0
-------------------+---------------------------------
  critical value   | -1.107639838348388


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentNeuN4>=0.950828 :
>  p = .00048828
Test of hypothesis Ho: QualityTreatmentNeuN4<=0.950828 :
>  p = .99975586
Test of hypothesis Ho: QualityTreatmentNeuN4==0.950828 :
>  p = .00097656

. signrank  AVotingCutOffNeutral4=44

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           1          39
    negative |       11          77          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffNeutral4 = 44
             z =  -2.981
    Prob > |z| =   0.0029

. permtest1  AVotingCutOffNeutral4=44
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffNeutral4-44
-------------------+---------------------------------
 observations      | 12
  - positive       | 1
  - negative       | 11
  - zero           | 0
-------------------+---------------------------------
  critical value   | -180.9875001907349


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffNeutral4>=44 : p = .
> 00048828
Test of hypothesis Ho: AVotingCutOffNeutral4<=44 : p = .
> 99975586
Test of hypothesis Ho: AVotingCutOffNeutral4==44 : p = .
> 00097656

. 
. /////////When Partisan Bias was Neutral and There were
>  5 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVNeutral5=mean(Willi
> ngness2Vote) if Neutral==1&HowManyHaveExpertise==5
(1155 missing values generated)

. by ElectorateID, sort: egen AvergesNeutral5=mean(MeanW
> TVNeutral5)
(207 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffNeutral5=Averg
> esNeutral5 if _n==1
(1,250 missing values generated)

. gen QualityTreatmentNeuN5=1-0.5*(1-AVotingCutOffNeutra
> l5/100)^5
(1,250 missing values generated)

. mean AVotingCutOffNeutral5

Mean estimation                   Number of obs   =     
>     10

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
AVotingCutOffNeutral5 |      28.63   3.575815      20.54
> 094                                                   
>        36.71906
--------------------------------------------------------
> ---------------

. mean QualityTreatmentNeuN5

Mean estimation                   Number of obs   =     
>     10

--------------------------------------------------------
> ---------------
                      |       Mean   Std. Err.     [95% 
> Con                                                   
>    f. Interval]
----------------------+---------------------------------
> ---------------
QualityTreatmentNeuN5 |    .887612   .0234631      .8345
> 348                                                   
>        .9406893
--------------------------------------------------------
> ---------------

. signrank QualityTreatmentNeuN5=0.953074

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           4        27.5
    negative |        9          51        27.5
        zero |        0           0           0
-------------+---------------------------------
         all |       10          55          55

unadjusted variance       96.25
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         96.25

Ho: QualityTreatmentNeuN5 = 0.953074
             z =  -2.395
    Prob > |z| =   0.0166

. permtest1 QualityTreatmentNeuN5=0.953074
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentNeuN5-0.953074
-------------------+---------------------------------
 observations      | 10
  - positive       | 1
  - negative       | 9
  - zero           | 0
-------------------+---------------------------------
  critical value   | -.6546197307014461


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentNeuN5>=0.953074 :
>  p = .00878906
Test of hypothesis Ho: QualityTreatmentNeuN5<=0.953074 :
>  p = .9921875
Test of hypothesis Ho: QualityTreatmentNeuN5==0.953074 :
>  p = .01757813

. signrank  AVotingCutOffNeutral5=37.7

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           7        27.5
    negative |        9          48        27.5
        zero |        0           0           0
-------------+---------------------------------
         all |       10          55          55

unadjusted variance       96.25
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance         96.25

Ho: AVotingCutOffNeutral5 = 37.7
             z =  -2.090
    Prob > |z| =   0.0367

. permtest1  AVotingCutOffNeutral5=37.7
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffNeutral5-37.7
-------------------+---------------------------------
 observations      | 10
  - positive       | 1
  - negative       | 9
  - zero           | 0
-------------------+---------------------------------
  critical value   | -90.69999885559085


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffNeutral5>=37.7 : p =
>  .01660156
Test of hypothesis Ho: AVotingCutOffNeutral5<=37.7 : p =
>  .984375
Test of hypothesis Ho: AVotingCutOffNeutral5==37.7 : p =
>  .03320313

. 
. 
. /////////When Partisan Bias was Supportive and There w
> as 1 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVSupportive1=mean(Wi
> llingness2Vote) if Supportive==1&HowManyHaveExpertise=
> =1
(1258 missing values generated)

. by ElectorateID, sort: egen AvergesSupportive1=mean(Me
> anWTVSupportive1)
(1158 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffSupportive1=Av
> ergesSupportive1 if _n==1
(1,259 missing values generated)

. gen QualityTreatmentSuppN1=1

. mean AVotingCutOffSupportive1

Mean estimation                   Number of obs   =     
>      1

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive1 |       37.5          .        
>      .                                                
>                  .
--------------------------------------------------------
> ------------------

. signrank AVotingCutOffSupportive1=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        1           1          .5
    negative |        0           0          .5
        zero |        0           0           0
-------------+---------------------------------
         all |        1           1           1

unadjusted variance        0.25
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance          0.25

Ho: AVotingCutOffSupportive1 = 0
             z =   1.000
    Prob > |z| =   0.3173

. permtest1 AVotingCutOffSupportive1=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffSupportive1-0
-------------------+---------------------------------
 observations      | 1
  - positive       | 1
  - negative       | 0
  - zero           | 0
-------------------+---------------------------------
  critical value   | 37.5


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffSupportive1>=0 : p =
>  1
Test of hypothesis Ho: AVotingCutOffSupportive1<=0 : p =
>  .5
Test of hypothesis Ho: AVotingCutOffSupportive1==0 : p =
>  1

. 
. 
. /////////When Partisan Bias was Supportive and There w
> ere 2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVSupportive2=mean(Wi
> llingness2Vote) if Supportive==1&HowManyHaveExpertise=
> =2
(1230 missing values generated)

. by ElectorateID, sort: egen AvergesSupportive2=mean(Me
> anWTVSupportive2)
(209 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffSupportive2=Av
> ergesSupportive2 if _n==1
(1,250 missing values generated)

. gen QualityTreatmentSuppN2=1

. mean AVotingCutOffSupportive2

Mean estimation                   Number of obs   =     
>     10

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive2 |       8.35   2.636601      2.
> 385593                                                
>           14.31441
--------------------------------------------------------
> ------------------

. signrank AVotingCutOffSupportive2=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        9          54          27
    negative |        0           0          27
        zero |        1           1           1
-------------+---------------------------------
         all |       10          55          55

unadjusted variance       96.25
adjustment for ties       -0.13
adjustment for zeros      -0.25
                     ----------
adjusted variance         95.88

Ho: AVotingCutOffSupportive2 = 0
             z =   2.757
    Prob > |z| =   0.0058

. permtest1 AVotingCutOffSupportive2=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffSupportive2-0
-------------------+---------------------------------
 observations      | 10
  - positive       | 9
  - negative       | 0
  - zero           | 1
-------------------+---------------------------------
  critical value   | 83.5


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffSupportive2>=0 : p =
>  1
Test of hypothesis Ho: AVotingCutOffSupportive2<=0 : p =
>  .00195313
Test of hypothesis Ho: AVotingCutOffSupportive2==0 : p =
>  .00390625

. 
. /////////When Partisan Bias was Supportive and There w
> ere 2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVSupportive3=mean(Wi
> llingness2Vote) if Supportive==1&HowManyHaveExpertise=
> =3
(1125 missing values generated)

. by ElectorateID, sort: egen AvergesSupportive3=mean(Me
> anWTVSupportive3)

. by ElectorateID, sort: gen AVotingCutOffSupportive3=Av
> ergesSupportive3 if _n==1
(1,248 missing values generated)

. gen QualityTreatmentSuppN3=1

. mean AVotingCutOffSupportive3

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive3 |   16.18843   2.983253       9
> .62233                                                
>           22.75452
--------------------------------------------------------
> ------------------

. signrank AVotingCutOffSupportive3=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |       12          78          39
    negative |        0           0          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffSupportive3 = 0
             z =   3.059
    Prob > |z| =   0.0022

. permtest1 AVotingCutOffSupportive3=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffSupportive3-0
-------------------+---------------------------------
 observations      | 12
  - positive       | 12
  - negative       | 0
  - zero           | 0
-------------------+---------------------------------
  critical value   | 194.2611126899719


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffSupportive3>=0 : p =
>  1
Test of hypothesis Ho: AVotingCutOffSupportive3<=0 : p =
>  .00024414
Test of hypothesis Ho: AVotingCutOffSupportive3==0 : p =
>  .00048828

. 
. /////////When Partisan Bias was Supportive and There w
> ere 2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVSupportive4=mean(Wi
> llingness2Vote) if Supportive==1&HowManyHaveExpertise=
> =4
(1120 missing values generated)

. by ElectorateID, sort: egen AvergesSupportive4=mean(Me
> anWTVSupportive4)

. by ElectorateID, sort: gen AVotingCutOffSupportive4=Av
> ergesSupportive4 if _n==1
(1,248 missing values generated)

. gen QualityTreatmentSuppN4=1

. mean AVotingCutOffSupportive4

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive4 |   11.72535   1.928021      7.
> 481802                                                
>           15.96889
--------------------------------------------------------
> ------------------

. signrank AVotingCutOffSupportive4=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |       12          78          39
    negative |        0           0          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffSupportive4 = 0
             z =   3.059
    Prob > |z| =   0.0022

. permtest1 AVotingCutOffSupportive4=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffSupportive4-0
-------------------+---------------------------------
 observations      | 12
  - positive       | 12
  - negative       | 0
  - zero           | 0
-------------------+---------------------------------
  critical value   | 140.7041683197021


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffSupportive4>=0 : p =
>  1
Test of hypothesis Ho: AVotingCutOffSupportive4<=0 : p =
>  .00024414
Test of hypothesis Ho: AVotingCutOffSupportive4==0 : p =
>  .00048828

. 
. /////////When Partisan Bias was Supportive and There w
> ere 2 Expert Voter////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVSupportive5=mean(Wi
> llingness2Vote) if Supportive==1&HowManyHaveExpertise=
> =5
(1155 missing values generated)

. by ElectorateID, sort: egen AvergesSupportive5=mean(Me
> anWTVSupportive5)
(103 missing values generated)

. by ElectorateID, sort: gen AVotingCutOffSupportive5=Av
> ergesSupportive5 if _n==1
(1,249 missing values generated)

. gen QualityTreatmentSuppN5=1

. mean AVotingCutOffSupportive5

Mean estimation                   Number of obs   =     
>     11

--------------------------------------------------------
> ------------------
                         |       Mean   Std. Err.     [9
> 5% Con                                                
>       f. Interval]
-------------------------+------------------------------
> ------------------
AVotingCutOffSupportive5 |   13.09091   3.413748      5.
> 484604                                                
>           20.69721
--------------------------------------------------------
> ------------------

. signrank AVotingCutOffSupportive5=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |       11          66          33
    negative |        0           0          33
        zero |        0           0           0
-------------+---------------------------------
         all |       11          66          66

unadjusted variance      126.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        126.50

Ho: AVotingCutOffSupportive5 = 0
             z =   2.934
    Prob > |z| =   0.0033

. permtest1 AVotingCutOffSupportive5=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffSupportive5-0
-------------------+---------------------------------
 observations      | 11
  - positive       | 11
  - negative       | 0
  - zero           | 0
-------------------+---------------------------------
  critical value   | 143.9999990463257


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffSupportive5>=0 : p =
>  1
Test of hypothesis Ho: AVotingCutOffSupportive5<=0 : p =
>  .00048828
Test of hypothesis Ho: AVotingCutOffSupportive5==0 : p =
>  .00097656

. 
. restore

. 
. 
. 
. preserve

. *Now we focus on the behavior of expert voters in the 
> Control Group
. drop if Expertise==0
(1,089 observations deleted)

. drop if Treatment=="TreatmentGroup"
(1,260 observations deleted)

. 
. //////////      When the partisan bias is Against     
>  //////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVAgainst=mean(Willin
> gness2Vote) if Against==1
(788 missing values generated)

. by ElectorateID, sort: egen AvergesAgainst=mean(MeanWT
> VAgainst)

. by ElectorateID, sort: gen AVotingCutOffAgainst=Averge
> sAgainst if _n==1
(1,239 missing values generated)

. gen QualityTreatmentAga=comb(5,3)*(0.7*(AVotingCutOffA
> gainst/100))^3*(1-(0.7*(AVotingCutOffAgainst/100)))^2+
> comb(5,4)*(0.7*(AVotingCutOffAgainst/100))^4*(1-(0.7*(
> AVotingCutOffAgainst/100)))^1+comb(5,5)*(0.7*(AVotingC
> utOffAgainst/100))^5+0.5*comb(5,2)*((0.7*(AVotingCutOf
> fAgainst/100))^2)*(1-(0.7*(AVotingCutOffAgainst/100)))
> ^3
(1,239 missing values generated)

. mean AVotingCutOffAgainst

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> --------------
                     |       Mean   Std. Err.     [95% C
> on                                                    
>   f. Interval]
---------------------+----------------------------------
> --------------
AVotingCutOffAgainst |   51.82489   2.911182      45.417
> 42                                                    
>       58.23236
--------------------------------------------------------
> --------------

. mean QualityTreatmentAga

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> -------------
                    |       Mean   Std. Err.     [95% Co
> n                                                     
>  f. Interval]
--------------------+-----------------------------------
> -------------
QualityTreatmentAga |    .425564   .0346559      .349286
> 9                                                     
>      .5018412
--------------------------------------------------------
> -------------

. signrank QualityTreatmentAga=0.878986

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          39
    negative |       12          78          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: QualityTreatmentAga = 0.878986
             z =  -3.059
    Prob > |z| =   0.0022

. permtest1 QualityTreatmentAga=0.878986
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentAga-0.878986
-------------------+---------------------------------
 observations      | 12
  - positive       | 0
  - negative       | 12
  - zero           | 0
-------------------+---------------------------------
  critical value   | -5.4410634068079


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentAga>=0.878986 : p
>  = .00024414
Test of hypothesis Ho: QualityTreatmentAga<=0.878986 : p
>  = 1
Test of hypothesis Ho: QualityTreatmentAga==0.878986 : p
>  = .00048828

. signrank  AVotingCutOffAgainst=96.2

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        0           0          39
    negative |       12          78          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffAgainst = 96.2
             z =  -3.059
    Prob > |z| =   0.0022

. permtest1  AVotingCutOffAgainst=96.2
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffAgainst-96.2
-------------------+---------------------------------
 observations      | 12
  - positive       | 0
  - negative       | 12
  - zero           | 0
-------------------+---------------------------------
  critical value   | -532.5013145446778


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffAgainst>=96.2 : p = 
> .00024414
Test of hypothesis Ho: AVotingCutOffAgainst<=96.2 : p = 
> 1
Test of hypothesis Ho: AVotingCutOffAgainst==96.2 : p = 
> .00048828

. 
. //////////      When the partisan bias is Neutral     
>  //////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVNeutral=mean(Willin
> gness2Vote) if Neutral==1
(859 missing values generated)

. by ElectorateID, sort: egen AvergesNeutral=mean(MeanWT
> VNeutral)

. by ElectorateID, sort: gen AVotingCutOffNeutral=Averge
> sNeutral if _n==1
(1,239 missing values generated)

. gen QualityTreatmentNeu=comb(5,1)*(0.7*(AVotingCutOffN
> eutral/100))*(1-(0.7*(AVotingCutOffNeutral/100)))^4+co
> mb(5,2)*(0.7*(AVotingCutOffNeutral/100))^2*(1-(0.7*(AV
> otingCutOffNeutral/100)))^3+comb(5,3)*(0.7*(AVotingCut
> OffNeutral/100))^3*(1-(0.7*(AVotingCutOffNeutral/100))
> )^2+comb(5,4)*(0.7*(AVotingCutOffNeutral/100))^4*(1-(0
> .7*(AVotingCutOffNeutral/100)))^1+comb(5,5)*(0.7*(AVot
> ingCutOffNeutral/100))^5+0.5*comb(5,0)*((0.7*(AVotingC
> utOffNeutral/100))^0)*(1-(0.7*(AVotingCutOffNeutral/10
> 0)))^5
(1,239 missing values generated)

. mean AVotingCutOffNeutral

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> --------------
                     |       Mean   Std. Err.     [95% C
> on                                                    
>   f. Interval]
---------------------+----------------------------------
> --------------
AVotingCutOffNeutral |   47.46382   3.245181      40.321
> 22                                                    
>       54.60641
--------------------------------------------------------
> --------------

. mean QualityTreatmentNeu

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> -------------
                    |       Mean   Std. Err.     [95% Co
> n                                                     
>  f. Interval]
--------------------+-----------------------------------
> -------------
QualityTreatmentNeu |   .9246114   .0137732      .894296
> 9                                                     
>       .954926
--------------------------------------------------------
> -------------

. signrank QualityTreatmentNeu=0.93614

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        6          34          39
    negative |        6          44          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: QualityTreatmentNeu = 0.93614
             z =  -0.392
    Prob > |z| =   0.6949

. permtest1 QualityTreatmentNeu=0.93614
Fisher-Pitman permutation test for paired replicates


 difference vector | QualityTreatmentNeu-0.93614
-------------------+---------------------------------
 observations      | 12
  - positive       | 6
  - negative       | 6
  - zero           | 0
-------------------+---------------------------------
  critical value   | -.1383426091003416


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: QualityTreatmentNeu>=0.93614 : p 
> = .24584961
Test of hypothesis Ho: QualityTreatmentNeu<=0.93614 : p 
> = .75439453
Test of hypothesis Ho: QualityTreatmentNeu==0.93614 : p 
> = .49169922

. signrank  AVotingCutOffNeutral=48.2

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |        6          38          39
    negative |        6          40          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffNeutral = 48.2
             z =  -0.078
    Prob > |z| =   0.9375

. permtest1  AVotingCutOffNeutral=48.2
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffNeutral-48.2
-------------------+---------------------------------
 observations      | 12
  - positive       | 6
  - negative       | 6
  - zero           | 0
-------------------+---------------------------------
  critical value   | -8.834202194213901


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffNeutral>=48.2 : p = 
> .41259766
Test of hypothesis Ho: AVotingCutOffNeutral<=48.2 : p = 
> .58764648
Test of hypothesis Ho: AVotingCutOffNeutral==48.2 : p = 
> .82519531

. 
. 
. //////////      When the partisan bias is Supportive  
>     //////////
> sort ElectorateID

. by ElectorateID, sort: egen MeanWTVSupportive=mean(Wil
> lingness2Vote) if Supportive==1
(855 missing values generated)

. by ElectorateID, sort: egen AvergesSupportive=mean(Mea
> nWTVSupportive)

. by ElectorateID, sort: gen AVotingCutOffSupportive=Ave
> rgesSupportive if _n==1
(1,239 missing values generated)

. gen QualityTreatmentSupp=1

. mean AVotingCutOffSupportive

Mean estimation                   Number of obs   =     
>     12

--------------------------------------------------------
> -----------------
                        |       Mean   Std. Err.     [95
> % Con                                                 
>      f. Interval]
------------------------+-------------------------------
> -----------------
AVotingCutOffSupportive |   21.72267   3.187422       14
> .7072                                                 
>          28.73813
--------------------------------------------------------
> -----------------

. 
. signrank  AVotingCutOffSupportive=0

Wilcoxon signed-rank test

        sign |      obs   sum ranks    expected
-------------+---------------------------------
    positive |       12          78          39
    negative |        0           0          39
        zero |        0           0           0
-------------+---------------------------------
         all |       12          78          78

unadjusted variance      162.50
adjustment for ties        0.00
adjustment for zeros       0.00
                     ----------
adjusted variance        162.50

Ho: AVotingCutOffSupportive = 0
             z =   3.059
    Prob > |z| =   0.0022

. permtest1  AVotingCutOffSupportive=0
Fisher-Pitman permutation test for paired replicates


 difference vector | AVotingCutOffSupportive-0
-------------------+---------------------------------
 observations      | 12
  - positive       | 12
  - negative       | 0
  - zero           | 0
-------------------+---------------------------------
  critical value   | 260.6719813346863


mode of operation:  exact (complete permutation)

Test of hypothesis Ho: AVotingCutOffSupportive>=0 : p = 
> 1
Test of hypothesis Ho: AVotingCutOffSupportive<=0 : p = 
> .00024414
Test of hypothesis Ho: AVotingCutOffSupportive==0 : p = 
> .00048828

. 
. restore

. log close PSRM
      name:  PSRM
       log:  D:\Replication.log
  log type:  text
 closed on:   2 Oct 2021, 18:06:42
--------------------------------------------------------
